id	sid	tid	token	lemma	pos
ejpam-5846	1	1	european	european	PROPN
ejpam-5846	1	2	journal	journal	PROPN
ejpam-5846	1	3	of	of	ADP
ejpam-5846	1	4	pure	pure	ADJ
ejpam-5846	1	5	and	and	CCONJ
ejpam-5846	1	6	applied	applied	ADJ
ejpam-5846	1	7	mathematics	mathematic	NOUN
ejpam-5846	1	8	2025	2025	NUM
ejpam-5846	1	9	,	,	PUNCT
ejpam-5846	1	10	vol	vol	NOUN
ejpam-5846	1	11	.	.	PROPN
ejpam-5846	1	12	18	18	NUM
ejpam-5846	1	13	,	,	PUNCT
ejpam-5846	1	14	issue	issue	NOUN
ejpam-5846	1	15	1	1	NUM
ejpam-5846	1	16	,	,	PUNCT
ejpam-5846	1	17	article	article	NOUN
ejpam-5846	1	18	number	number	NOUN
ejpam-5846	1	19	5846	5846	NUM
ejpam-5846	1	20	issn	issn	VERB
ejpam-5846	1	21	1307	1307	NUM
ejpam-5846	1	22	-	-	SYM
ejpam-5846	1	23	5543	5543	NUM
ejpam-5846	1	24	–	–	PUNCT
ejpam-5846	1	25	ejpam.com	ejpam.com	X
ejpam-5846	1	26	published	publish	VERB
ejpam-5846	1	27	by	by	ADP
ejpam-5846	1	28	new	new	PROPN
ejpam-5846	1	29	york	york	PROPN
ejpam-5846	1	30	business	business	PROPN
ejpam-5846	1	31	global	global	ADJ
ejpam-5846	1	32	solving	solve	VERB
ejpam-5846	1	33	geometric	geometric	ADJ
ejpam-5846	1	34	problems	problem	NOUN
ejpam-5846	1	35	by	by	ADP
ejpam-5846	1	36	introducing	introduce	VERB
ejpam-5846	1	37	an	an	DET
ejpam-5846	1	38	equilateral	equilateral	ADJ
ejpam-5846	1	39	triangle	triangle	NOUN
ejpam-5846	1	40	samed	samed	PROPN
ejpam-5846	1	41	j.	j.	PROPN
ejpam-5846	1	42	aliyev1,∗	aliyev1,∗	PROPN
ejpam-5846	1	43	,	,	PUNCT
ejpam-5846	1	44	maftun	maftun	PROPN
ejpam-5846	1	45	n.	n.	PROPN
ejpam-5846	1	46	heydarova2	heydarova2	PROPN
ejpam-5846	1	47	,	,	PUNCT
ejpam-5846	1	48	aynura	aynura	NOUN
ejpam-5846	1	49	m.	m.	NOUN
ejpam-5846	1	50	seyidova3	seyidova3	PROPN
ejpam-5846	1	51	1	1	NUM
ejpam-5846	1	52	department	department	NOUN
ejpam-5846	1	53	of	of	ADP
ejpam-5846	1	54	mathematics	mathematic	NOUN
ejpam-5846	1	55	and	and	CCONJ
ejpam-5846	1	56	methods	method	NOUN
ejpam-5846	1	57	of	of	ADP
ejpam-5846	1	58	its	its	PRON
ejpam-5846	1	59	teaching	teaching	NOUN
ejpam-5846	1	60	,	,	PUNCT
ejpam-5846	1	61	faculty	faculty	NOUN
ejpam-5846	1	62	of	of	ADP
ejpam-5846	1	63	mechanics	mechanic	NOUN
ejpam-5846	1	64	and	and	CCONJ
ejpam-5846	1	65	mathematics	mathematic	NOUN
ejpam-5846	1	66	,	,	PUNCT
ejpam-5846	1	67	baku	baku	PROPN
ejpam-5846	1	68	state	state	PROPN
ejpam-5846	1	69	university	university	PROPN
ejpam-5846	1	70	,	,	PUNCT
ejpam-5846	1	71	baku	baku	PROPN
ejpam-5846	1	72	,	,	PUNCT
ejpam-5846	1	73	z.khalilov	z.khalilov	PROPN
ejpam-5846	1	74	str	str	NOUN
ejpam-5846	1	75	.	.	PROPN
ejpam-5846	2	1	23	23	NUM
ejpam-5846	2	2	,	,	PUNCT
ejpam-5846	2	3	az	az	PROPN
ejpam-5846	2	4	1148	1148	NUM
ejpam-5846	2	5	,	,	PUNCT
ejpam-5846	2	6	azerbaijan	azerbaijan	PROPN
ejpam-5846	2	7	2	2	NUM
ejpam-5846	2	8	department	department	NOUN
ejpam-5846	2	9	of	of	ADP
ejpam-5846	2	10	mathematics	mathematics	PROPN
ejpam-5846	2	11	and	and	CCONJ
ejpam-5846	2	12	informatics	informatic	NOUN
ejpam-5846	2	13	teaching	teach	VERB
ejpam-5846	2	14	technology	technology	NOUN
ejpam-5846	2	15	,	,	PUNCT
ejpam-5846	2	16	faculty	faculty	NOUN
ejpam-5846	2	17	of	of	ADP
ejpam-5846	2	18	mathematics	mathematic	NOUN
ejpam-5846	2	19	,	,	PUNCT
ejpam-5846	2	20	sumgait	sumgait	VERB
ejpam-5846	2	21	state	state	PROPN
ejpam-5846	2	22	university	university	PROPN
ejpam-5846	2	23	,	,	PUNCT
ejpam-5846	2	24	sumgait	sumgait	NOUN
ejpam-5846	2	25	,	,	PUNCT
ejpam-5846	2	26	district	district	NOUN
ejpam-5846	2	27	43	43	NUM
ejpam-5846	2	28	,	,	PUNCT
ejpam-5846	2	29	az	az	PROPN
ejpam-5846	2	30	5008	5008	NUM
ejpam-5846	2	31	,	,	PUNCT
ejpam-5846	2	32	azerbaijan	azerbaijan	PROPN
ejpam-5846	2	33	3	3	NUM
ejpam-5846	2	34	department	department	PROPN
ejpam-5846	2	35	of	of	ADP
ejpam-5846	2	36	general	general	ADJ
ejpam-5846	2	37	mathematics	mathematics	PROPN
ejpam-5846	2	38	,	,	PUNCT
ejpam-5846	2	39	faculty	faculty	NOUN
ejpam-5846	2	40	of	of	ADP
ejpam-5846	2	41	physics	physics	NOUN
ejpam-5846	2	42	and	and	CCONJ
ejpam-5846	2	43	mathematics	mathematic	NOUN
ejpam-5846	2	44	,	,	PUNCT
ejpam-5846	2	45	nakhchivan	nakhchivan	PROPN
ejpam-5846	2	46	state	state	PROPN
ejpam-5846	2	47	university	university	PROPN
ejpam-5846	2	48	az	az	PROPN
ejpam-5846	2	49	7012	7012	NUM
ejpam-5846	2	50	,	,	PUNCT
ejpam-5846	2	51	university	university	NOUN
ejpam-5846	2	52	campus	campus	NOUN
ejpam-5846	2	53	,	,	PUNCT
ejpam-5846	2	54	nakhchivan	nakhchivan	PROPN
ejpam-5846	2	55	city	city	PROPN
ejpam-5846	2	56	,	,	PUNCT
ejpam-5846	2	57	azerbaijan	azerbaijan	PROPN
ejpam-5846	2	58	abstract	abstract	NOUN
ejpam-5846	2	59	.	.	PUNCT
ejpam-5846	3	1	the	the	DET
ejpam-5846	3	2	article	article	NOUN
ejpam-5846	3	3	focuses	focus	VERB
ejpam-5846	3	4	on	on	ADP
ejpam-5846	3	5	using	use	VERB
ejpam-5846	3	6	an	an	DET
ejpam-5846	3	7	equilateral	equilateral	ADJ
ejpam-5846	3	8	triangle	triangle	NOUN
ejpam-5846	3	9	as	as	ADP
ejpam-5846	3	10	an	an	DET
ejpam-5846	3	11	auxiliary	auxiliary	ADJ
ejpam-5846	3	12	element	element	NOUN
ejpam-5846	3	13	in	in	ADP
ejpam-5846	3	14	solving	solve	VERB
ejpam-5846	3	15	geometric	geometric	ADJ
ejpam-5846	3	16	(	(	PUNCT
ejpam-5846	3	17	planimetric	planimetric	ADJ
ejpam-5846	3	18	)	)	PUNCT
ejpam-5846	3	19	problems	problem	NOUN
ejpam-5846	3	20	.	.	PUNCT
ejpam-5846	4	1	this	this	DET
ejpam-5846	4	2	method	method	NOUN
ejpam-5846	4	3	aims	aim	VERB
ejpam-5846	4	4	to	to	PART
ejpam-5846	4	5	simplify	simplify	VERB
ejpam-5846	4	6	the	the	DET
ejpam-5846	4	7	problem	problem	NOUN
ejpam-5846	4	8	-	-	PUNCT
ejpam-5846	4	9	solving	solve	VERB
ejpam-5846	4	10	process	process	NOUN
ejpam-5846	4	11	and	and	CCONJ
ejpam-5846	4	12	make	make	VERB
ejpam-5846	4	13	it	it	PRON
ejpam-5846	4	14	more	more	ADV
ejpam-5846	4	15	intuitive	intuitive	ADJ
ejpam-5846	4	16	by	by	ADP
ejpam-5846	4	17	introducing	introduce	VERB
ejpam-5846	4	18	an	an	DET
ejpam-5846	4	19	equilateral	equilateral	ADJ
ejpam-5846	4	20	triangle	triangle	NOUN
ejpam-5846	4	21	in	in	ADP
ejpam-5846	4	22	specific	specific	ADJ
ejpam-5846	4	23	scenarios	scenario	NOUN
ejpam-5846	4	24	.	.	PUNCT
ejpam-5846	5	1	by	by	ADP
ejpam-5846	5	2	adding	add	VERB
ejpam-5846	5	3	this	this	DET
ejpam-5846	5	4	triangle	triangle	NOUN
ejpam-5846	5	5	,	,	PUNCT
ejpam-5846	5	6	the	the	DET
ejpam-5846	5	7	relationships	relationship	NOUN
ejpam-5846	5	8	between	between	ADP
ejpam-5846	5	9	known	known	ADJ
ejpam-5846	5	10	and	and	CCONJ
ejpam-5846	5	11	unknown	unknown	ADJ
ejpam-5846	5	12	quantities	quantity	NOUN
ejpam-5846	5	13	in	in	ADP
ejpam-5846	5	14	the	the	DET
ejpam-5846	5	15	problem	problem	NOUN
ejpam-5846	5	16	become	become	VERB
ejpam-5846	5	17	more	more	ADV
ejpam-5846	5	18	apparent	apparent	ADJ
ejpam-5846	5	19	or	or	CCONJ
ejpam-5846	5	20	even	even	ADV
ejpam-5846	5	21	obvious	obvious	ADJ
ejpam-5846	5	22	.	.	PUNCT
ejpam-5846	6	1	the	the	DET
ejpam-5846	6	2	paper	paper	NOUN
ejpam-5846	6	3	discusses	discuss	VERB
ejpam-5846	6	4	four	four	NUM
ejpam-5846	6	5	different	different	ADJ
ejpam-5846	6	6	scenarios	scenario	NOUN
ejpam-5846	6	7	where	where	SCONJ
ejpam-5846	6	8	this	this	DET
ejpam-5846	6	9	method	method	NOUN
ejpam-5846	6	10	can	can	AUX
ejpam-5846	6	11	be	be	AUX
ejpam-5846	6	12	applied	apply	VERB
ejpam-5846	6	13	,	,	PUNCT
ejpam-5846	6	14	illustrating	illustrate	VERB
ejpam-5846	6	15	each	each	DET
ejpam-5846	6	16	case	case	NOUN
ejpam-5846	6	17	with	with	ADP
ejpam-5846	6	18	sample	sample	NOUN
ejpam-5846	6	19	problems	problem	NOUN
ejpam-5846	6	20	.	.	PUNCT
ejpam-5846	7	1	the	the	DET
ejpam-5846	7	2	elegance	elegance	NOUN
ejpam-5846	7	3	and	and	CCONJ
ejpam-5846	7	4	utility	utility	NOUN
ejpam-5846	7	5	of	of	ADP
ejpam-5846	7	6	the	the	DET
ejpam-5846	7	7	method	method	NOUN
ejpam-5846	7	8	in	in	ADP
ejpam-5846	7	9	enhancing	enhance	VERB
ejpam-5846	7	10	the	the	DET
ejpam-5846	7	11	solution	solution	NOUN
ejpam-5846	7	12	process	process	NOUN
ejpam-5846	7	13	are	be	AUX
ejpam-5846	7	14	highlighted	highlight	VERB
ejpam-5846	7	15	.	.	PUNCT
ejpam-5846	8	1	in	in	ADP
ejpam-5846	8	2	this	this	DET
ejpam-5846	8	3	context	context	NOUN
ejpam-5846	8	4	,	,	PUNCT
ejpam-5846	8	5	the	the	DET
ejpam-5846	8	6	applicability	applicability	NOUN
ejpam-5846	8	7	of	of	ADP
ejpam-5846	8	8	this	this	DET
ejpam-5846	8	9	method	method	NOUN
ejpam-5846	8	10	in	in	ADP
ejpam-5846	8	11	various	various	ADJ
ejpam-5846	8	12	olympiad	olympiad	NOUN
ejpam-5846	8	13	problems	problem	NOUN
ejpam-5846	8	14	or	or	CCONJ
ejpam-5846	8	15	more	more	ADV
ejpam-5846	8	16	complex	complex	ADJ
ejpam-5846	8	17	geometric	geometric	ADJ
ejpam-5846	8	18	problems	problem	NOUN
ejpam-5846	8	19	is	be	AUX
ejpam-5846	8	20	demonstrated	demonstrate	VERB
ejpam-5846	8	21	.	.	PUNCT
ejpam-5846	9	1	this	this	DET
ejpam-5846	9	2	approach	approach	NOUN
ejpam-5846	9	3	often	often	ADV
ejpam-5846	9	4	reduces	reduce	VERB
ejpam-5846	9	5	problems	problem	NOUN
ejpam-5846	9	6	to	to	ADP
ejpam-5846	9	7	simpler	simple	ADJ
ejpam-5846	9	8	forms	form	NOUN
ejpam-5846	9	9	,	,	PUNCT
ejpam-5846	9	10	saving	save	VERB
ejpam-5846	9	11	time	time	NOUN
ejpam-5846	9	12	and	and	CCONJ
ejpam-5846	9	13	effort	effort	NOUN
ejpam-5846	9	14	in	in	ADP
ejpam-5846	9	15	finding	find	VERB
ejpam-5846	9	16	solutions	solution	NOUN
ejpam-5846	9	17	.	.	PUNCT
ejpam-5846	10	1	the	the	DET
ejpam-5846	10	2	paper	paper	NOUN
ejpam-5846	10	3	provides	provide	VERB
ejpam-5846	10	4	evidence	evidence	NOUN
ejpam-5846	10	5	of	of	ADP
ejpam-5846	10	6	the	the	DET
ejpam-5846	10	7	method	method	NOUN
ejpam-5846	10	8	’s	’s	PART
ejpam-5846	10	9	effectiveness	effectiveness	NOUN
ejpam-5846	10	10	and	and	CCONJ
ejpam-5846	10	11	offers	offer	VERB
ejpam-5846	10	12	guidance	guidance	NOUN
ejpam-5846	10	13	on	on	ADP
ejpam-5846	10	14	its	its	PRON
ejpam-5846	10	15	application	application	NOUN
ejpam-5846	10	16	.	.	PUNCT
ejpam-5846	11	1	2020	2020	NUM
ejpam-5846	11	2	mathematics	mathematic	NOUN
ejpam-5846	11	3	subject	subject	NOUN
ejpam-5846	11	4	classifications	classification	NOUN
ejpam-5846	11	5	:	:	PUNCT
ejpam-5846	11	6	97g10	97g10	NUM
ejpam-5846	11	7	,	,	PUNCT
ejpam-5846	11	8	97g30	97g30	NUM
ejpam-5846	11	9	,	,	PUNCT
ejpam-5846	11	10	97g40	97g40	NUM
ejpam-5846	11	11	key	key	ADJ
ejpam-5846	11	12	words	word	NOUN
ejpam-5846	11	13	and	and	CCONJ
ejpam-5846	11	14	phrases	phrase	NOUN
ejpam-5846	11	15	:	:	PUNCT
ejpam-5846	11	16	planimetric	planimetric	ADJ
ejpam-5846	11	17	problem	problem	NOUN
ejpam-5846	11	18	,	,	PUNCT
ejpam-5846	11	19	equilateral	equilateral	ADJ
ejpam-5846	11	20	triangle	triangle	NOUN
ejpam-5846	11	21	,	,	PUNCT
ejpam-5846	11	22	isosceles	isoscele	NOUN
ejpam-5846	11	23	triangle	triangle	NOUN
ejpam-5846	11	24	,	,	PUNCT
ejpam-5846	11	25	auxiliary	auxiliary	ADJ
ejpam-5846	11	26	element	element	NOUN
ejpam-5846	11	27	1	1	NUM
ejpam-5846	11	28	.	.	PUNCT
ejpam-5846	12	1	introduction	introduction	NOUN
ejpam-5846	12	2	in	in	ADP
ejpam-5846	12	3	the	the	DET
ejpam-5846	12	4	study	study	NOUN
ejpam-5846	12	5	of	of	ADP
ejpam-5846	12	6	geometry	geometry	NOUN
ejpam-5846	12	7	,	,	PUNCT
ejpam-5846	12	8	especially	especially	ADV
ejpam-5846	12	9	in	in	ADP
ejpam-5846	12	10	competitive	competitive	ADJ
ejpam-5846	12	11	problem	problem	NOUN
ejpam-5846	12	12	-	-	PUNCT
ejpam-5846	12	13	solving	solve	VERB
ejpam-5846	12	14	settings	setting	NOUN
ejpam-5846	12	15	,	,	PUNCT
ejpam-5846	12	16	understanding	understanding	NOUN
ejpam-5846	12	17	and	and	CCONJ
ejpam-5846	12	18	identifying	identify	VERB
ejpam-5846	12	19	the	the	DET
ejpam-5846	12	20	relationships	relationship	NOUN
ejpam-5846	12	21	between	between	ADP
ejpam-5846	12	22	known	known	ADJ
ejpam-5846	12	23	and	and	CCONJ
ejpam-5846	12	24	unknown	unknown	ADJ
ejpam-5846	12	25	quantities	quantity	NOUN
ejpam-5846	12	26	within	within	ADP
ejpam-5846	12	27	a	a	DET
ejpam-5846	12	28	given	give	VERB
ejpam-5846	12	29	problem	problem	NOUN
ejpam-5846	12	30	is	be	AUX
ejpam-5846	12	31	crucial	crucial	ADJ
ejpam-5846	12	32	yet	yet	ADV
ejpam-5846	12	33	challenging	challenging	ADJ
ejpam-5846	12	34	.	.	PUNCT
ejpam-5846	13	1	such	such	ADJ
ejpam-5846	13	2	problems	problem	NOUN
ejpam-5846	13	3	often	often	ADV
ejpam-5846	13	4	require	require	VERB
ejpam-5846	13	5	deeper	deep	ADJ
ejpam-5846	13	6	insight	insight	NOUN
ejpam-5846	13	7	and	and	CCONJ
ejpam-5846	13	8	inventive	inventive	ADJ
ejpam-5846	13	9	approaches	approach	NOUN
ejpam-5846	13	10	to	to	PART
ejpam-5846	13	11	unravel	unravel	VERB
ejpam-5846	13	12	the	the	DET
ejpam-5846	13	13	hidden	hidden	ADJ
ejpam-5846	13	14	structures	structure	NOUN
ejpam-5846	13	15	and	and	CCONJ
ejpam-5846	13	16	properties	property	NOUN
ejpam-5846	13	17	of	of	ADP
ejpam-5846	13	18	geometric	geometric	ADJ
ejpam-5846	13	19	shapes	shape	NOUN
ejpam-5846	13	20	.	.	PUNCT
ejpam-5846	14	1	the	the	DET
ejpam-5846	14	2	introduction	introduction	NOUN
ejpam-5846	14	3	of	of	ADP
ejpam-5846	14	4	auxiliary	auxiliary	ADJ
ejpam-5846	14	5	elements	element	NOUN
ejpam-5846	14	6	,	,	PUNCT
ejpam-5846	14	7	such	such	ADJ
ejpam-5846	14	8	as	as	ADP
ejpam-5846	14	9	additional	additional	ADJ
ejpam-5846	14	10	lines	line	NOUN
ejpam-5846	14	11	or	or	CCONJ
ejpam-5846	14	12	figures	figure	NOUN
ejpam-5846	14	13	,	,	PUNCT
ejpam-5846	14	14	has	have	AUX
ejpam-5846	14	15	proven	prove	VERB
ejpam-5846	14	16	to	to	PART
ejpam-5846	14	17	be	be	AUX
ejpam-5846	14	18	an	an	DET
ejpam-5846	14	19	effective	effective	ADJ
ejpam-5846	14	20	strategy	strategy	NOUN
ejpam-5846	14	21	for	for	ADP
ejpam-5846	14	22	making	make	VERB
ejpam-5846	14	23	these	these	DET
ejpam-5846	14	24	underlying	underlie	VERB
ejpam-5846	14	25	relationships	relationship	NOUN
ejpam-5846	14	26	more	more	ADV
ejpam-5846	14	27	accessible	accessible	ADJ
ejpam-5846	14	28	and	and	CCONJ
ejpam-5846	14	29	apparent	apparent	ADJ
ejpam-5846	14	30	.	.	PUNCT
ejpam-5846	15	1	by	by	ADP
ejpam-5846	15	2	introducing	introduce	VERB
ejpam-5846	15	3	auxiliary	auxiliary	ADJ
ejpam-5846	15	4	constructions	construction	NOUN
ejpam-5846	15	5	,	,	PUNCT
ejpam-5846	15	6	it	it	PRON
ejpam-5846	15	7	is	be	AUX
ejpam-5846	15	8	often	often	ADV
ejpam-5846	15	9	possible	possible	ADJ
ejpam-5846	15	10	to	to	PART
ejpam-5846	15	11	reduce	reduce	VERB
ejpam-5846	15	12	a	a	DET
ejpam-5846	15	13	complex	complex	ADJ
ejpam-5846	15	14	∗corresponding	∗corresponding	NOUN
ejpam-5846	15	15	author	author	NOUN
ejpam-5846	15	16	.	.	PUNCT
ejpam-5846	16	1	doi	doi	NOUN
ejpam-5846	16	2	:	:	PUNCT
ejpam-5846	16	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5846	https://doi.org/10.29020/nybg.ejpam.v18i1.5846	NOUN
ejpam-5846	16	4	email	email	NOUN
ejpam-5846	16	5	addresses	address	NOUN
ejpam-5846	16	6	:	:	PUNCT
ejpam-5846	16	7	samed59@bk.ru	samed59@bk.ru	PROPN
ejpam-5846	16	8	(	(	PUNCT
ejpam-5846	16	9	s.	s.	PROPN
ejpam-5846	16	10	j.	j.	PROPN
ejpam-5846	16	11	aliyev	aliyev	PROPN
ejpam-5846	16	12	)	)	PUNCT
ejpam-5846	16	13	,	,	PUNCT
ejpam-5846	16	14	maftun.heydarova@sdu.edu.az	maftun.heydarova@sdu.edu.az	X
ejpam-5846	16	15	(	(	PUNCT
ejpam-5846	16	16	m.	m.	NOUN
ejpam-5846	16	17	n.	n.	PROPN
ejpam-5846	16	18	heydarova	heydarova	PROPN
ejpam-5846	16	19	)	)	PUNCT
ejpam-5846	16	20	,	,	PUNCT
ejpam-5846	16	21	aynureseyidova@ndu.edu.az	aynureseyidova@ndu.edu.az	NOUN
ejpam-5846	16	22	(	(	PUNCT
ejpam-5846	16	23	a.	a.	NOUN
ejpam-5846	16	24	m.	m.	PROPN
ejpam-5846	16	25	seyidova	seyidova	PROPN
ejpam-5846	16	26	)	)	PUNCT
ejpam-5846	16	27	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5846	16	28	1	1	NUM
ejpam-5846	16	29	copyright	copyright	NOUN
ejpam-5846	16	30	:	:	PUNCT
ejpam-5846	17	1	©	©	PROPN
ejpam-5846	17	2	2025	2025	NUM
ejpam-5846	17	3	the	the	DET
ejpam-5846	17	4	author(s	author(s	NOUN
ejpam-5846	17	5	)	)	PUNCT
ejpam-5846	17	6	.	.	PUNCT
ejpam-5846	18	1	(	(	PUNCT
ejpam-5846	18	2	cc	cc	NOUN
ejpam-5846	18	3	by	by	ADP
ejpam-5846	18	4	-	-	PUNCT
ejpam-5846	18	5	nc	nc	PROPN
ejpam-5846	18	6	4.0	4.0	NUM
ejpam-5846	18	7	)	)	PUNCT
ejpam-5846	18	8	s.	s.	PROPN
ejpam-5846	18	9	j.	j.	PROPN
ejpam-5846	18	10	aliyev	aliyev	PROPN
ejpam-5846	18	11	,	,	PUNCT
ejpam-5846	18	12	m.	m.	PROPN
ejpam-5846	18	13	n.	n.	PROPN
ejpam-5846	18	14	heydarova	heydarova	PROPN
ejpam-5846	18	15	,	,	PUNCT
ejpam-5846	18	16	a.	a.	NOUN
ejpam-5846	18	17	m.	m.	PROPN
ejpam-5846	18	18	seyidova	seyidova	PROPN
ejpam-5846	18	19	/	/	SYM
ejpam-5846	18	20	eur	eur	PROPN
ejpam-5846	18	21	.	.	PUNCT
ejpam-5846	19	1	j.	j.	PROPN
ejpam-5846	19	2	pure	pure	PROPN
ejpam-5846	19	3	appl	appl	PROPN
ejpam-5846	19	4	.	.	PROPN
ejpam-5846	19	5	math	math	PROPN
ejpam-5846	19	6	,	,	PUNCT
ejpam-5846	19	7	18	18	NUM
ejpam-5846	19	8	(	(	PUNCT
ejpam-5846	19	9	1	1	NUM
ejpam-5846	19	10	)	)	PUNCT
ejpam-5846	19	11	(	(	PUNCT
ejpam-5846	19	12	2025	2025	NUM
ejpam-5846	19	13	)	)	PUNCT
ejpam-5846	19	14	,	,	PUNCT
ejpam-5846	19	15	5846	5846	NUM
ejpam-5846	19	16	2	2	NUM
ejpam-5846	19	17	of	of	ADP
ejpam-5846	19	18	9	9	NUM
ejpam-5846	19	19	problem	problem	NOUN
ejpam-5846	19	20	to	to	ADP
ejpam-5846	19	21	one	one	NUM
ejpam-5846	19	22	that	that	PRON
ejpam-5846	19	23	is	be	AUX
ejpam-5846	19	24	simpler	simple	ADJ
ejpam-5846	19	25	and	and	CCONJ
ejpam-5846	19	26	,	,	PUNCT
ejpam-5846	19	27	in	in	ADP
ejpam-5846	19	28	some	some	DET
ejpam-5846	19	29	cases	case	NOUN
ejpam-5846	19	30	,	,	PUNCT
ejpam-5846	19	31	more	more	ADV
ejpam-5846	19	32	familiar	familiar	ADJ
ejpam-5846	19	33	,	,	PUNCT
ejpam-5846	19	34	allowing	allow	VERB
ejpam-5846	19	35	the	the	DET
ejpam-5846	19	36	solver	solver	NOUN
ejpam-5846	19	37	to	to	PART
ejpam-5846	19	38	apply	apply	VERB
ejpam-5846	19	39	known	know	VERB
ejpam-5846	19	40	theorems	theorem	NOUN
ejpam-5846	19	41	and	and	CCONJ
ejpam-5846	19	42	methods	method	NOUN
ejpam-5846	19	43	more	more	ADV
ejpam-5846	19	44	effectively	effectively	ADV
ejpam-5846	19	45	.	.	PUNCT
ejpam-5846	20	1	in	in	ADP
ejpam-5846	20	2	this	this	DET
ejpam-5846	20	3	paper	paper	NOUN
ejpam-5846	20	4	,	,	PUNCT
ejpam-5846	20	5	we	we	PRON
ejpam-5846	20	6	explore	explore	VERB
ejpam-5846	20	7	the	the	DET
ejpam-5846	20	8	method	method	NOUN
ejpam-5846	20	9	of	of	ADP
ejpam-5846	20	10	introducing	introduce	VERB
ejpam-5846	20	11	an	an	DET
ejpam-5846	20	12	equilateral	equilateral	ADJ
ejpam-5846	20	13	triangle	triangle	NOUN
ejpam-5846	20	14	as	as	ADP
ejpam-5846	20	15	an	an	DET
ejpam-5846	20	16	auxiliary	auxiliary	ADJ
ejpam-5846	20	17	element	element	NOUN
ejpam-5846	20	18	in	in	ADP
ejpam-5846	20	19	solving	solve	VERB
ejpam-5846	20	20	planimetric	planimetric	ADJ
ejpam-5846	20	21	problems	problem	NOUN
ejpam-5846	20	22	,	,	PUNCT
ejpam-5846	20	23	demonstrating	demonstrate	VERB
ejpam-5846	20	24	its	its	PRON
ejpam-5846	20	25	versatility	versatility	NOUN
ejpam-5846	20	26	and	and	CCONJ
ejpam-5846	20	27	utility	utility	NOUN
ejpam-5846	20	28	in	in	ADP
ejpam-5846	20	29	various	various	ADJ
ejpam-5846	20	30	problem	problem	NOUN
ejpam-5846	20	31	scenarios	scenario	NOUN
ejpam-5846	20	32	.	.	PUNCT
ejpam-5846	21	1	the	the	DET
ejpam-5846	21	2	equilateral	equilateral	ADJ
ejpam-5846	21	3	triangle	triangle	NOUN
ejpam-5846	21	4	holds	hold	VERB
ejpam-5846	21	5	particular	particular	ADJ
ejpam-5846	21	6	appeal	appeal	NOUN
ejpam-5846	21	7	in	in	ADP
ejpam-5846	21	8	geometry	geometry	NOUN
ejpam-5846	21	9	due	due	ADP
ejpam-5846	21	10	to	to	ADP
ejpam-5846	21	11	its	its	PRON
ejpam-5846	21	12	inherent	inherent	ADJ
ejpam-5846	21	13	symmetry	symmetry	NOUN
ejpam-5846	21	14	and	and	CCONJ
ejpam-5846	21	15	well	well	ADV
ejpam-5846	21	16	-	-	PUNCT
ejpam-5846	21	17	defined	define	VERB
ejpam-5846	21	18	properties	property	NOUN
ejpam-5846	21	19	,	,	PUNCT
ejpam-5846	21	20	which	which	PRON
ejpam-5846	21	21	can	can	AUX
ejpam-5846	21	22	simplify	simplify	VERB
ejpam-5846	21	23	the	the	DET
ejpam-5846	21	24	problem	problem	NOUN
ejpam-5846	21	25	structure	structure	NOUN
ejpam-5846	21	26	when	when	SCONJ
ejpam-5846	21	27	appropriately	appropriately	ADV
ejpam-5846	21	28	incorporated	incorporate	VERB
ejpam-5846	21	29	.	.	PUNCT
ejpam-5846	22	1	however	however	ADV
ejpam-5846	22	2	,	,	PUNCT
ejpam-5846	22	3	identifying	identify	VERB
ejpam-5846	22	4	the	the	DET
ejpam-5846	22	5	appropriate	appropriate	ADJ
ejpam-5846	22	6	placement	placement	NOUN
ejpam-5846	22	7	and	and	CCONJ
ejpam-5846	22	8	alignment	alignment	NOUN
ejpam-5846	22	9	of	of	ADP
ejpam-5846	22	10	an	an	DET
ejpam-5846	22	11	equilateral	equilateral	ADJ
ejpam-5846	22	12	triangle	triangle	NOUN
ejpam-5846	22	13	is	be	AUX
ejpam-5846	22	14	not	not	PART
ejpam-5846	22	15	always	always	ADV
ejpam-5846	22	16	straightforward	straightforward	ADJ
ejpam-5846	22	17	,	,	PUNCT
ejpam-5846	22	18	as	as	SCONJ
ejpam-5846	22	19	this	this	PRON
ejpam-5846	22	20	often	often	ADV
ejpam-5846	22	21	requires	require	VERB
ejpam-5846	22	22	both	both	PRON
ejpam-5846	22	23	experience	experience	NOUN
ejpam-5846	22	24	and	and	CCONJ
ejpam-5846	22	25	geometric	geometric	ADJ
ejpam-5846	22	26	intuition	intuition	NOUN
ejpam-5846	22	27	.	.	PUNCT
ejpam-5846	23	1	when	when	SCONJ
ejpam-5846	23	2	successfully	successfully	ADV
ejpam-5846	23	3	applied	apply	VERB
ejpam-5846	23	4	,	,	PUNCT
ejpam-5846	23	5	this	this	DET
ejpam-5846	23	6	method	method	NOUN
ejpam-5846	23	7	not	not	PART
ejpam-5846	23	8	only	only	ADV
ejpam-5846	23	9	clarifies	clarify	VERB
ejpam-5846	23	10	complex	complex	ADJ
ejpam-5846	23	11	relationships	relationship	NOUN
ejpam-5846	23	12	but	but	CCONJ
ejpam-5846	23	13	also	also	ADV
ejpam-5846	23	14	leads	lead	VERB
ejpam-5846	23	15	to	to	ADP
ejpam-5846	23	16	elegant	elegant	ADJ
ejpam-5846	23	17	and	and	CCONJ
ejpam-5846	23	18	concise	concise	ADJ
ejpam-5846	23	19	solutions	solution	NOUN
ejpam-5846	23	20	,	,	PUNCT
ejpam-5846	23	21	reducing	reduce	VERB
ejpam-5846	23	22	otherwise	otherwise	ADV
ejpam-5846	23	23	intricate	intricate	ADJ
ejpam-5846	23	24	problems	problem	NOUN
ejpam-5846	23	25	to	to	ADP
ejpam-5846	23	26	a	a	DET
ejpam-5846	23	27	series	series	NOUN
ejpam-5846	23	28	of	of	ADP
ejpam-5846	23	29	elementary	elementary	ADJ
ejpam-5846	23	30	steps	step	NOUN
ejpam-5846	23	31	.	.	PUNCT
ejpam-5846	24	1	the	the	DET
ejpam-5846	24	2	concept	concept	NOUN
ejpam-5846	24	3	of	of	ADP
ejpam-5846	24	4	using	use	VERB
ejpam-5846	24	5	equilateral	equilateral	ADJ
ejpam-5846	24	6	triangles	triangle	NOUN
ejpam-5846	24	7	as	as	SCONJ
ejpam-5846	24	8	auxiliary	auxiliary	ADJ
ejpam-5846	24	9	elements	element	NOUN
ejpam-5846	24	10	is	be	AUX
ejpam-5846	24	11	grounded	ground	VERB
ejpam-5846	24	12	in	in	ADP
ejpam-5846	24	13	classical	classical	ADJ
ejpam-5846	24	14	geometry	geometry	NOUN
ejpam-5846	24	15	but	but	CCONJ
ejpam-5846	24	16	finds	find	VERB
ejpam-5846	24	17	renewed	renew	VERB
ejpam-5846	24	18	relevance	relevance	NOUN
ejpam-5846	24	19	in	in	ADP
ejpam-5846	24	20	the	the	DET
ejpam-5846	24	21	context	context	NOUN
ejpam-5846	24	22	of	of	ADP
ejpam-5846	24	23	mathematical	mathematical	ADJ
ejpam-5846	24	24	competitions	competition	NOUN
ejpam-5846	24	25	and	and	CCONJ
ejpam-5846	24	26	advanced	advanced	ADJ
ejpam-5846	24	27	geometry	geometry	NOUN
ejpam-5846	24	28	education	education	NOUN
ejpam-5846	24	29	.	.	PUNCT
ejpam-5846	25	1	studies	study	NOUN
ejpam-5846	25	2	have	have	AUX
ejpam-5846	25	3	shown	show	VERB
ejpam-5846	25	4	that	that	SCONJ
ejpam-5846	25	5	auxiliary	auxiliary	ADJ
ejpam-5846	25	6	constructions	construction	NOUN
ejpam-5846	25	7	,	,	PUNCT
ejpam-5846	25	8	such	such	ADJ
ejpam-5846	25	9	as	as	ADP
ejpam-5846	25	10	the	the	DET
ejpam-5846	25	11	addition	addition	NOUN
ejpam-5846	25	12	of	of	ADP
ejpam-5846	25	13	equilateral	equilateral	ADJ
ejpam-5846	25	14	triangles	triangle	NOUN
ejpam-5846	25	15	,	,	PUNCT
ejpam-5846	25	16	foster	foster	ADJ
ejpam-5846	25	17	intuitive	intuitive	ADJ
ejpam-5846	25	18	problem	problem	NOUN
ejpam-5846	25	19	-	-	PUNCT
ejpam-5846	25	20	solving	solve	VERB
ejpam-5846	25	21	skills	skill	NOUN
ejpam-5846	25	22	,	,	PUNCT
ejpam-5846	25	23	helping	help	VERB
ejpam-5846	25	24	learners	learner	NOUN
ejpam-5846	25	25	grasp	grasp	VERB
ejpam-5846	25	26	abstract	abstract	ADJ
ejpam-5846	25	27	geometric	geometric	ADJ
ejpam-5846	25	28	principles	principle	NOUN
ejpam-5846	25	29	in	in	ADP
ejpam-5846	25	30	a	a	DET
ejpam-5846	25	31	more	more	ADV
ejpam-5846	25	32	concrete	concrete	ADJ
ejpam-5846	25	33	manner	manner	NOUN
ejpam-5846	25	34	.	.	PUNCT
ejpam-5846	26	1	as	as	ADP
ejpam-5846	26	2	such	such	ADJ
ejpam-5846	26	3	,	,	PUNCT
ejpam-5846	26	4	this	this	DET
ejpam-5846	26	5	method	method	NOUN
ejpam-5846	26	6	can	can	AUX
ejpam-5846	26	7	serve	serve	VERB
ejpam-5846	26	8	as	as	ADP
ejpam-5846	26	9	a	a	DET
ejpam-5846	26	10	pedagogical	pedagogical	ADJ
ejpam-5846	26	11	tool	tool	NOUN
ejpam-5846	26	12	for	for	ADP
ejpam-5846	26	13	enhancing	enhance	VERB
ejpam-5846	26	14	students	student	NOUN
ejpam-5846	26	15	’	’	PART
ejpam-5846	26	16	understanding	understanding	NOUN
ejpam-5846	26	17	of	of	ADP
ejpam-5846	26	18	geometric	geometric	ADJ
ejpam-5846	26	19	concepts	concept	NOUN
ejpam-5846	26	20	and	and	CCONJ
ejpam-5846	26	21	improving	improve	VERB
ejpam-5846	26	22	their	their	PRON
ejpam-5846	26	23	analytical	analytical	ADJ
ejpam-5846	26	24	skills	skill	NOUN
ejpam-5846	26	25	.	.	PUNCT
ejpam-5846	27	1	by	by	ADP
ejpam-5846	27	2	applying	apply	VERB
ejpam-5846	27	3	the	the	DET
ejpam-5846	27	4	equilateral	equilateral	ADJ
ejpam-5846	27	5	triangle	triangle	NOUN
ejpam-5846	27	6	method	method	NOUN
ejpam-5846	27	7	,	,	PUNCT
ejpam-5846	27	8	solvers	solver	NOUN
ejpam-5846	27	9	can	can	AUX
ejpam-5846	27	10	often	often	ADV
ejpam-5846	27	11	identify	identify	VERB
ejpam-5846	27	12	pathways	pathway	NOUN
ejpam-5846	27	13	to	to	ADP
ejpam-5846	27	14	solutions	solution	NOUN
ejpam-5846	27	15	that	that	PRON
ejpam-5846	27	16	might	might	AUX
ejpam-5846	27	17	not	not	PART
ejpam-5846	27	18	be	be	AUX
ejpam-5846	27	19	apparent	apparent	ADJ
ejpam-5846	27	20	through	through	ADP
ejpam-5846	27	21	conventional	conventional	ADJ
ejpam-5846	27	22	methods	method	NOUN
ejpam-5846	27	23	alone	alone	ADV
ejpam-5846	27	24	.	.	PUNCT
ejpam-5846	28	1	the	the	DET
ejpam-5846	28	2	structure	structure	NOUN
ejpam-5846	28	3	of	of	ADP
ejpam-5846	28	4	this	this	DET
ejpam-5846	28	5	paper	paper	NOUN
ejpam-5846	28	6	is	be	AUX
ejpam-5846	28	7	organized	organize	VERB
ejpam-5846	28	8	as	as	SCONJ
ejpam-5846	28	9	follows	follow	VERB
ejpam-5846	28	10	:	:	PUNCT
ejpam-5846	28	11	we	we	PRON
ejpam-5846	28	12	begin	begin	VERB
ejpam-5846	28	13	by	by	ADP
ejpam-5846	28	14	discussing	discuss	VERB
ejpam-5846	28	15	the	the	DET
ejpam-5846	28	16	theoretical	theoretical	ADJ
ejpam-5846	28	17	foundation	foundation	NOUN
ejpam-5846	28	18	and	and	CCONJ
ejpam-5846	28	19	conditions	condition	NOUN
ejpam-5846	28	20	under	under	ADP
ejpam-5846	28	21	which	which	PRON
ejpam-5846	28	22	the	the	DET
ejpam-5846	28	23	equilateral	equilateral	ADJ
ejpam-5846	28	24	triangle	triangle	NOUN
ejpam-5846	28	25	method	method	NOUN
ejpam-5846	28	26	can	can	AUX
ejpam-5846	28	27	be	be	AUX
ejpam-5846	28	28	applied	apply	VERB
ejpam-5846	28	29	.	.	PUNCT
ejpam-5846	29	1	then	then	ADV
ejpam-5846	29	2	,	,	PUNCT
ejpam-5846	29	3	we	we	PRON
ejpam-5846	29	4	categorize	categorize	VERB
ejpam-5846	29	5	and	and	CCONJ
ejpam-5846	29	6	illustrate	illustrate	VERB
ejpam-5846	29	7	four	four	NUM
ejpam-5846	29	8	specific	specific	ADJ
ejpam-5846	29	9	situations	situation	NOUN
ejpam-5846	29	10	in	in	ADP
ejpam-5846	29	11	which	which	PRON
ejpam-5846	29	12	an	an	DET
ejpam-5846	29	13	equilateral	equilateral	ADJ
ejpam-5846	29	14	triangle	triangle	NOUN
ejpam-5846	29	15	can	can	AUX
ejpam-5846	29	16	be	be	AUX
ejpam-5846	29	17	introduced	introduce	VERB
ejpam-5846	29	18	to	to	PART
ejpam-5846	29	19	aid	aid	VERB
ejpam-5846	29	20	in	in	ADP
ejpam-5846	29	21	solving	solve	VERB
ejpam-5846	29	22	a	a	DET
ejpam-5846	29	23	problem	problem	NOUN
ejpam-5846	29	24	.	.	PUNCT
ejpam-5846	30	1	each	each	DET
ejpam-5846	30	2	category	category	NOUN
ejpam-5846	30	3	is	be	AUX
ejpam-5846	30	4	supported	support	VERB
ejpam-5846	30	5	by	by	ADP
ejpam-5846	30	6	sample	sample	NOUN
ejpam-5846	30	7	problems	problem	NOUN
ejpam-5846	30	8	,	,	PUNCT
ejpam-5846	30	9	which	which	PRON
ejpam-5846	30	10	highlight	highlight	VERB
ejpam-5846	30	11	the	the	DET
ejpam-5846	30	12	method	method	NOUN
ejpam-5846	30	13	’s	’s	PART
ejpam-5846	30	14	effectiveness	effectiveness	NOUN
ejpam-5846	30	15	and	and	CCONJ
ejpam-5846	30	16	its	its	PRON
ejpam-5846	30	17	potential	potential	NOUN
ejpam-5846	30	18	for	for	ADP
ejpam-5846	30	19	simplifying	simplify	VERB
ejpam-5846	30	20	even	even	ADV
ejpam-5846	30	21	the	the	DET
ejpam-5846	30	22	most	most	ADV
ejpam-5846	30	23	challenging	challenging	ADJ
ejpam-5846	30	24	problems	problem	NOUN
ejpam-5846	30	25	.	.	PUNCT
ejpam-5846	31	1	lastly	lastly	ADV
ejpam-5846	31	2	,	,	PUNCT
ejpam-5846	31	3	we	we	PRON
ejpam-5846	31	4	provide	provide	VERB
ejpam-5846	31	5	insights	insight	NOUN
ejpam-5846	31	6	into	into	ADP
ejpam-5846	31	7	how	how	SCONJ
ejpam-5846	31	8	this	this	DET
ejpam-5846	31	9	method	method	NOUN
ejpam-5846	31	10	may	may	AUX
ejpam-5846	31	11	be	be	AUX
ejpam-5846	31	12	further	far	ADV
ejpam-5846	31	13	utilized	utilize	VERB
ejpam-5846	31	14	in	in	ADP
ejpam-5846	31	15	various	various	ADJ
ejpam-5846	31	16	educational	educational	ADJ
ejpam-5846	31	17	and	and	CCONJ
ejpam-5846	31	18	competitive	competitive	ADJ
ejpam-5846	31	19	contexts	contexts	NOUN
ejpam-5846	31	20	,	,	PUNCT
ejpam-5846	31	21	with	with	ADP
ejpam-5846	31	22	suggestions	suggestion	NOUN
ejpam-5846	31	23	for	for	ADP
ejpam-5846	31	24	future	future	ADJ
ejpam-5846	31	25	research	research	NOUN
ejpam-5846	31	26	and	and	CCONJ
ejpam-5846	31	27	applications	application	NOUN
ejpam-5846	31	28	.	.	PUNCT
ejpam-5846	32	1	this	this	DET
ejpam-5846	32	2	study	study	NOUN
ejpam-5846	32	3	aims	aim	VERB
ejpam-5846	32	4	to	to	PART
ejpam-5846	32	5	contribute	contribute	VERB
ejpam-5846	32	6	to	to	ADP
ejpam-5846	32	7	the	the	DET
ejpam-5846	32	8	field	field	NOUN
ejpam-5846	32	9	of	of	ADP
ejpam-5846	32	10	geometric	geometric	ADJ
ejpam-5846	32	11	problem	problem	NOUN
ejpam-5846	32	12	-	-	PUNCT
ejpam-5846	32	13	solving	solving	NOUN
ejpam-5846	32	14	by	by	ADP
ejpam-5846	32	15	offering	offer	VERB
ejpam-5846	32	16	a	a	DET
ejpam-5846	32	17	systematic	systematic	ADJ
ejpam-5846	32	18	approach	approach	NOUN
ejpam-5846	32	19	to	to	ADP
ejpam-5846	32	20	using	use	VERB
ejpam-5846	32	21	equilateral	equilateral	ADJ
ejpam-5846	32	22	triangles	triangle	NOUN
ejpam-5846	32	23	as	as	ADP
ejpam-5846	32	24	a	a	DET
ejpam-5846	32	25	powerful	powerful	ADJ
ejpam-5846	32	26	tool	tool	NOUN
ejpam-5846	32	27	in	in	ADP
ejpam-5846	32	28	the	the	DET
ejpam-5846	32	29	solver	solver	NOUN
ejpam-5846	32	30	’s	’s	PART
ejpam-5846	32	31	toolkit	toolkit	NOUN
ejpam-5846	32	32	.	.	PUNCT
ejpam-5846	33	1	it	it	PRON
ejpam-5846	33	2	is	be	AUX
ejpam-5846	33	3	our	our	PRON
ejpam-5846	33	4	hope	hope	NOUN
ejpam-5846	33	5	that	that	SCONJ
ejpam-5846	33	6	this	this	DET
ejpam-5846	33	7	method	method	NOUN
ejpam-5846	33	8	will	will	AUX
ejpam-5846	33	9	inspire	inspire	VERB
ejpam-5846	33	10	both	both	DET
ejpam-5846	33	11	educators	educator	NOUN
ejpam-5846	33	12	and	and	CCONJ
ejpam-5846	33	13	students	student	NOUN
ejpam-5846	33	14	to	to	PART
ejpam-5846	33	15	view	view	VERB
ejpam-5846	33	16	geometry	geometry	NOUN
ejpam-5846	33	17	problems	problem	NOUN
ejpam-5846	33	18	from	from	ADP
ejpam-5846	33	19	a	a	DET
ejpam-5846	33	20	new	new	ADJ
ejpam-5846	33	21	perspective	perspective	NOUN
ejpam-5846	33	22	,	,	PUNCT
ejpam-5846	33	23	encouraging	encourage	VERB
ejpam-5846	33	24	the	the	DET
ejpam-5846	33	25	creative	creative	ADJ
ejpam-5846	33	26	use	use	NOUN
ejpam-5846	33	27	of	of	ADP
ejpam-5846	33	28	auxiliary	auxiliary	ADJ
ejpam-5846	33	29	elements	element	NOUN
ejpam-5846	33	30	to	to	PART
ejpam-5846	33	31	uncover	uncover	VERB
ejpam-5846	33	32	elegant	elegant	ADJ
ejpam-5846	33	33	and	and	CCONJ
ejpam-5846	33	34	efficient	efficient	ADJ
ejpam-5846	33	35	solutions	solution	NOUN
ejpam-5846	33	36	.	.	PUNCT
ejpam-5846	34	1	the	the	DET
ejpam-5846	34	2	books	book	NOUN
ejpam-5846	34	3	[	[	X
ejpam-5846	34	4	7	7	NUM
ejpam-5846	34	5	,	,	PUNCT
ejpam-5846	34	6	8	8	NUM
ejpam-5846	34	7	]	]	PUNCT
ejpam-5846	34	8	details	detail	NOUN
ejpam-5846	34	9	classical	classical	ADJ
ejpam-5846	34	10	methods	method	NOUN
ejpam-5846	34	11	in	in	ADP
ejpam-5846	34	12	teaching	teaching	NOUN
ejpam-5846	34	13	geometry	geometry	NOUN
ejpam-5846	34	14	,	,	PUNCT
ejpam-5846	34	15	emphasizing	emphasize	VERB
ejpam-5846	34	16	the	the	DET
ejpam-5846	34	17	importance	importance	NOUN
ejpam-5846	34	18	of	of	ADP
ejpam-5846	34	19	auxiliary	auxiliary	ADJ
ejpam-5846	34	20	elements	element	NOUN
ejpam-5846	34	21	and	and	CCONJ
ejpam-5846	34	22	the	the	DET
ejpam-5846	34	23	relationships	relationship	NOUN
ejpam-5846	34	24	between	between	ADP
ejpam-5846	34	25	geometric	geometric	ADJ
ejpam-5846	34	26	shapes	shape	NOUN
ejpam-5846	34	27	.	.	PUNCT
ejpam-5846	35	1	it	it	PRON
ejpam-5846	35	2	encourages	encourage	VERB
ejpam-5846	35	3	the	the	DET
ejpam-5846	35	4	development	development	NOUN
ejpam-5846	35	5	of	of	ADP
ejpam-5846	35	6	intuitive	intuitive	ADJ
ejpam-5846	35	7	skills	skill	NOUN
ejpam-5846	35	8	in	in	ADP
ejpam-5846	35	9	problem	problem	NOUN
ejpam-5846	35	10	-	-	PUNCT
ejpam-5846	35	11	solving	solving	NOUN
ejpam-5846	35	12	,	,	PUNCT
ejpam-5846	35	13	especially	especially	ADV
ejpam-5846	35	14	in	in	ADP
ejpam-5846	35	15	planimetric	planimetric	ADJ
ejpam-5846	35	16	problems	problem	NOUN
ejpam-5846	35	17	,	,	PUNCT
ejpam-5846	35	18	by	by	ADP
ejpam-5846	35	19	highlighting	highlight	VERB
ejpam-5846	35	20	the	the	DET
ejpam-5846	35	21	role	role	NOUN
ejpam-5846	35	22	of	of	ADP
ejpam-5846	35	23	symmetry	symmetry	NOUN
ejpam-5846	35	24	and	and	CCONJ
ejpam-5846	35	25	structures	structure	NOUN
ejpam-5846	35	26	like	like	ADP
ejpam-5846	35	27	equilateral	equilateral	ADJ
ejpam-5846	35	28	and	and	CCONJ
ejpam-5846	35	29	isosceles	isoscele	NOUN
ejpam-5846	35	30	triangles	triangle	NOUN
ejpam-5846	35	31	.	.	PUNCT
ejpam-5846	36	1	the	the	DET
ejpam-5846	36	2	books	book	NOUN
ejpam-5846	36	3	[	[	X
ejpam-5846	36	4	6	6	NUM
ejpam-5846	36	5	,	,	PUNCT
ejpam-5846	36	6	10	10	NUM
ejpam-5846	36	7	]	]	PUNCT
ejpam-5846	36	8	details	detail	NOUN
ejpam-5846	36	9	how	how	SCONJ
ejpam-5846	36	10	to	to	PART
ejpam-5846	36	11	incorporate	incorporate	VERB
ejpam-5846	36	12	auxiliary	auxiliary	ADJ
ejpam-5846	36	13	elements	element	NOUN
ejpam-5846	36	14	and	and	CCONJ
ejpam-5846	36	15	position	position	NOUN
ejpam-5846	36	16	structures	structure	NOUN
ejpam-5846	36	17	effectively	effectively	ADV
ejpam-5846	36	18	.	.	PUNCT
ejpam-5846	37	1	it	it	PRON
ejpam-5846	37	2	highlights	highlight	VERB
ejpam-5846	37	3	how	how	SCONJ
ejpam-5846	37	4	even	even	ADV
ejpam-5846	37	5	simple	simple	ADJ
ejpam-5846	37	6	shapes	shape	NOUN
ejpam-5846	37	7	like	like	ADP
ejpam-5846	37	8	equilateral	equilateral	ADJ
ejpam-5846	37	9	triangles	triangle	NOUN
ejpam-5846	37	10	can	can	AUX
ejpam-5846	37	11	serve	serve	VERB
ejpam-5846	37	12	as	as	ADP
ejpam-5846	37	13	powerful	powerful	ADJ
ejpam-5846	37	14	aids	aid	NOUN
ejpam-5846	37	15	in	in	ADP
ejpam-5846	37	16	geometric	geometric	ADJ
ejpam-5846	37	17	problem	problem	NOUN
ejpam-5846	37	18	-	-	PUNCT
ejpam-5846	37	19	solving	solving	NOUN
ejpam-5846	37	20	.	.	PUNCT
ejpam-5846	38	1	the	the	DET
ejpam-5846	38	2	works	work	NOUN
ejpam-5846	38	3	[	[	X
ejpam-5846	38	4	1–4	1–4	NOUN
ejpam-5846	38	5	,	,	PUNCT
ejpam-5846	38	6	9	9	NUM
ejpam-5846	38	7	,	,	PUNCT
ejpam-5846	38	8	12	12	NUM
ejpam-5846	38	9	]	]	PUNCT
ejpam-5846	38	10	devoted	devote	VERB
ejpam-5846	38	11	to	to	ADP
ejpam-5846	38	12	the	the	DET
ejpam-5846	38	13	study	study	NOUN
ejpam-5846	38	14	of	of	ADP
ejpam-5846	38	15	geometric	geometric	ADJ
ejpam-5846	38	16	methods	method	NOUN
ejpam-5846	38	17	,	,	PUNCT
ejpam-5846	38	18	including	include	VERB
ejpam-5846	38	19	the	the	DET
ejpam-5846	38	20	method	method	ADJ
ejpam-5846	38	21	additional	additional	ADJ
ejpam-5846	38	22	constructions	construction	NOUN
ejpam-5846	38	23	.	.	PUNCT
ejpam-5846	39	1	in	in	ADP
ejpam-5846	39	2	these	these	DET
ejpam-5846	39	3	papers	paper	NOUN
ejpam-5846	39	4	,	,	PUNCT
ejpam-5846	39	5	the	the	DET
ejpam-5846	39	6	solution	solution	NOUN
ejpam-5846	39	7	of	of	ADP
ejpam-5846	39	8	some	some	DET
ejpam-5846	39	9	kinds	kind	NOUN
ejpam-5846	39	10	of	of	ADP
ejpam-5846	39	11	problems	problem	NOUN
ejpam-5846	39	12	is	be	AUX
ejpam-5846	39	13	presented	present	VERB
ejpam-5846	39	14	by	by	ADP
ejpam-5846	39	15	this	this	DET
ejpam-5846	39	16	method	method	NOUN
ejpam-5846	39	17	.	.	PUNCT
ejpam-5846	40	1	also	also	ADV
ejpam-5846	40	2	lets	let	VERB
ejpam-5846	40	3	mention	mention	VERB
ejpam-5846	40	4	[	[	X
ejpam-5846	40	5	5	5	NUM
ejpam-5846	40	6	]	]	PUNCT
ejpam-5846	40	7	,	,	PUNCT
ejpam-5846	40	8	co	co	VERB
ejpam-5846	40	9	-	-	VERB
ejpam-5846	40	10	authored	author	VERB
ejpam-5846	40	11	by	by	ADP
ejpam-5846	40	12	the	the	DET
ejpam-5846	40	13	first	first	ADJ
ejpam-5846	40	14	and	and	CCONJ
ejpam-5846	40	15	second	second	ADJ
ejpam-5846	40	16	authors	author	NOUN
ejpam-5846	40	17	,	,	PUNCT
ejpam-5846	40	18	s.	s.	PROPN
ejpam-5846	40	19	j.	j.	PROPN
ejpam-5846	40	20	aliyev	aliyev	PROPN
ejpam-5846	40	21	,	,	PUNCT
ejpam-5846	40	22	m.	m.	PROPN
ejpam-5846	40	23	n.	n.	PROPN
ejpam-5846	40	24	heydarova	heydarova	PROPN
ejpam-5846	40	25	,	,	PUNCT
ejpam-5846	40	26	a.	a.	NOUN
ejpam-5846	40	27	m.	m.	PROPN
ejpam-5846	40	28	seyidova	seyidova	PROPN
ejpam-5846	40	29	/	/	SYM
ejpam-5846	40	30	eur	eur	PROPN
ejpam-5846	40	31	.	.	PUNCT
ejpam-5846	41	1	j.	j.	PROPN
ejpam-5846	41	2	pure	pure	PROPN
ejpam-5846	41	3	appl	appl	PROPN
ejpam-5846	41	4	.	.	PROPN
ejpam-5846	41	5	math	math	PROPN
ejpam-5846	41	6	,	,	PUNCT
ejpam-5846	41	7	18	18	NUM
ejpam-5846	41	8	(	(	PUNCT
ejpam-5846	41	9	1	1	NUM
ejpam-5846	41	10	)	)	PUNCT
ejpam-5846	41	11	(	(	PUNCT
ejpam-5846	41	12	2025	2025	NUM
ejpam-5846	41	13	)	)	PUNCT
ejpam-5846	41	14	,	,	PUNCT
ejpam-5846	41	15	5846	5846	NUM
ejpam-5846	41	16	3	3	NUM
ejpam-5846	41	17	of	of	ADP
ejpam-5846	41	18	9	9	NUM
ejpam-5846	41	19	where	where	SCONJ
ejpam-5846	41	20	,	,	PUNCT
ejpam-5846	41	21	using	use	VERB
ejpam-5846	41	22	the	the	DET
ejpam-5846	41	23	circle	circle	NOUN
ejpam-5846	41	24	(	(	PUNCT
ejpam-5846	41	25	divided	divide	VERB
ejpam-5846	41	26	into	into	ADP
ejpam-5846	41	27	equal	equal	ADJ
ejpam-5846	41	28	parts	part	NOUN
ejpam-5846	41	29	)	)	PUNCT
ejpam-5846	41	30	as	as	ADP
ejpam-5846	41	31	an	an	DET
ejpam-5846	41	32	auxiliary	auxiliary	ADJ
ejpam-5846	41	33	element	element	NOUN
ejpam-5846	41	34	,	,	PUNCT
ejpam-5846	41	35	the	the	DET
ejpam-5846	41	36	solution	solution	NOUN
ejpam-5846	41	37	is	be	AUX
ejpam-5846	41	38	found	find	VERB
ejpam-5846	41	39	in	in	ADP
ejpam-5846	41	40	a	a	DET
ejpam-5846	41	41	quite	quite	ADV
ejpam-5846	41	42	simple	simple	ADJ
ejpam-5846	41	43	and	and	CCONJ
ejpam-5846	41	44	smart	smart	ADJ
ejpam-5846	41	45	way	way	NOUN
ejpam-5846	41	46	.	.	PUNCT
ejpam-5846	42	1	2	2	X
ejpam-5846	42	2	.	.	X
ejpam-5846	42	3	the	the	DET
ejpam-5846	42	4	method	method	NOUN
ejpam-5846	42	5	one	one	NUM
ejpam-5846	42	6	of	of	ADP
ejpam-5846	42	7	the	the	DET
ejpam-5846	42	8	interesting	interesting	ADJ
ejpam-5846	42	9	and	and	CCONJ
ejpam-5846	42	10	original	original	ADJ
ejpam-5846	42	11	ways	way	NOUN
ejpam-5846	42	12	of	of	ADP
ejpam-5846	42	13	solving	solve	VERB
ejpam-5846	42	14	planimetric	planimetric	ADJ
ejpam-5846	42	15	problems	problem	NOUN
ejpam-5846	42	16	is	be	AUX
ejpam-5846	42	17	the	the	DET
ejpam-5846	42	18	method	method	NOUN
ejpam-5846	42	19	of	of	ADP
ejpam-5846	42	20	introducing	introduce	VERB
ejpam-5846	42	21	an	an	DET
ejpam-5846	42	22	equilateral	equilateral	ADJ
ejpam-5846	42	23	triangle	triangle	NOUN
ejpam-5846	42	24	.	.	PUNCT
ejpam-5846	43	1	its	its	PRON
ejpam-5846	43	2	attractive	attractive	ADJ
ejpam-5846	43	3	sides	side	NOUN
ejpam-5846	43	4	are	be	AUX
ejpam-5846	43	5	brevity	brevity	NOUN
ejpam-5846	43	6	of	of	ADP
ejpam-5846	43	7	reasoning	reasoning	NOUN
ejpam-5846	43	8	,	,	PUNCT
ejpam-5846	43	9	external	external	ADJ
ejpam-5846	43	10	and	and	CCONJ
ejpam-5846	43	11	internal	internal	ADJ
ejpam-5846	43	12	beauty	beauty	NOUN
ejpam-5846	43	13	.	.	PUNCT
ejpam-5846	44	1	the	the	DET
ejpam-5846	44	2	essence	essence	NOUN
ejpam-5846	44	3	of	of	ADP
ejpam-5846	44	4	the	the	DET
ejpam-5846	44	5	method	method	NOUN
ejpam-5846	44	6	of	of	ADP
ejpam-5846	44	7	introducing	introduce	VERB
ejpam-5846	44	8	an	an	DET
ejpam-5846	44	9	equilateral	equilateral	ADJ
ejpam-5846	44	10	triangles	triangle	NOUN
ejpam-5846	44	11	lies	lie	VERB
ejpam-5846	44	12	in	in	ADP
ejpam-5846	44	13	the	the	DET
ejpam-5846	44	14	fact	fact	NOUN
ejpam-5846	44	15	that	that	SCONJ
ejpam-5846	44	16	you	you	PRON
ejpam-5846	44	17	add	add	VERB
ejpam-5846	44	18	some	some	DET
ejpam-5846	44	19	new	new	ADJ
ejpam-5846	44	20	(	(	PUNCT
ejpam-5846	44	21	auxiliary	auxiliary	ADJ
ejpam-5846	44	22	)	)	PUNCT
ejpam-5846	44	23	elements	element	NOUN
ejpam-5846	44	24	to	to	ADP
ejpam-5846	44	25	the	the	DET
ejpam-5846	44	26	drawing	drawing	NOUN
ejpam-5846	44	27	of	of	ADP
ejpam-5846	44	28	your	your	PRON
ejpam-5846	44	29	problem	problem	NOUN
ejpam-5846	44	30	.	.	PUNCT
ejpam-5846	45	1	as	as	ADP
ejpam-5846	45	2	a	a	DET
ejpam-5846	45	3	result	result	NOUN
ejpam-5846	45	4	,	,	PUNCT
ejpam-5846	45	5	the	the	DET
ejpam-5846	45	6	relationships	relationship	NOUN
ejpam-5846	45	7	between	between	ADP
ejpam-5846	45	8	the	the	DET
ejpam-5846	45	9	problem	problem	NOUN
ejpam-5846	45	10	data	datum	NOUN
ejpam-5846	45	11	and	and	CCONJ
ejpam-5846	45	12	unknown	unknown	ADJ
ejpam-5846	45	13	quantities	quantity	NOUN
ejpam-5846	45	14	,	,	PUNCT
ejpam-5846	45	15	which	which	PRON
ejpam-5846	45	16	have	have	AUX
ejpam-5846	45	17	been	be	AUX
ejpam-5846	45	18	hard	hard	ADJ
ejpam-5846	45	19	to	to	PART
ejpam-5846	45	20	see	see	VERB
ejpam-5846	45	21	before	before	ADV
ejpam-5846	45	22	,	,	PUNCT
ejpam-5846	45	23	become	become	VERB
ejpam-5846	45	24	more	more	ADV
ejpam-5846	45	25	tangible	tangible	ADJ
ejpam-5846	45	26	,	,	PUNCT
ejpam-5846	45	27	or	or	CCONJ
ejpam-5846	45	28	even	even	ADV
ejpam-5846	45	29	obvious	obvious	ADJ
ejpam-5846	45	30	.	.	PUNCT
ejpam-5846	46	1	equilateral	equilateral	ADJ
ejpam-5846	46	2	triangle	triangle	NOUN
ejpam-5846	46	3	can	can	AUX
ejpam-5846	46	4	be	be	AUX
ejpam-5846	46	5	introduced	introduce	VERB
ejpam-5846	46	6	in	in	ADP
ejpam-5846	46	7	the	the	DET
ejpam-5846	46	8	drawing	drawing	NOUN
ejpam-5846	46	9	of	of	ADP
ejpam-5846	46	10	a	a	DET
ejpam-5846	46	11	given	give	VERB
ejpam-5846	46	12	problem	problem	NOUN
ejpam-5846	46	13	as	as	SCONJ
ejpam-5846	46	14	follows	follow	VERB
ejpam-5846	46	15	:	:	PUNCT
ejpam-5846	46	16	situation	situation	NOUN
ejpam-5846	46	17	1	1	NUM
ejpam-5846	46	18	.	.	PUNCT
ejpam-5846	46	19	equilateral	equilateral	ADJ
ejpam-5846	46	20	triangle	triangle	NOUN
ejpam-5846	46	21	can	can	AUX
ejpam-5846	46	22	be	be	AUX
ejpam-5846	46	23	constructed	construct	VERB
ejpam-5846	46	24	in	in	ADP
ejpam-5846	46	25	the	the	DET
ejpam-5846	46	26	internal	internal	ADJ
ejpam-5846	46	27	domain	domain	NOUN
ejpam-5846	46	28	of	of	ADP
ejpam-5846	46	29	a	a	DET
ejpam-5846	46	30	given	give	VERB
ejpam-5846	46	31	problem	problem	NOUN
ejpam-5846	46	32	.	.	PUNCT
ejpam-5846	47	1	situation	situation	NOUN
ejpam-5846	47	2	2	2	NUM
ejpam-5846	47	3	.	.	X
ejpam-5846	47	4	equilateral	equilateral	ADJ
ejpam-5846	47	5	triangle	triangle	NOUN
ejpam-5846	47	6	can	can	AUX
ejpam-5846	47	7	be	be	AUX
ejpam-5846	47	8	constructed	construct	VERB
ejpam-5846	47	9	in	in	ADP
ejpam-5846	47	10	the	the	DET
ejpam-5846	47	11	external	external	ADJ
ejpam-5846	47	12	domain	domain	NOUN
ejpam-5846	47	13	of	of	ADP
ejpam-5846	47	14	a	a	DET
ejpam-5846	47	15	given	give	VERB
ejpam-5846	47	16	problem	problem	NOUN
ejpam-5846	47	17	.	.	PUNCT
ejpam-5846	48	1	situation	situation	NOUN
ejpam-5846	48	2	3	3	NUM
ejpam-5846	48	3	.	.	PUNCT
ejpam-5846	48	4	equilateral	equilateral	ADJ
ejpam-5846	48	5	triangle	triangle	NOUN
ejpam-5846	48	6	can	can	AUX
ejpam-5846	48	7	be	be	AUX
ejpam-5846	48	8	constructed	construct	VERB
ejpam-5846	48	9	so	so	SCONJ
ejpam-5846	48	10	that	that	SCONJ
ejpam-5846	48	11	it	it	PRON
ejpam-5846	48	12	includes	include	VERB
ejpam-5846	48	13	the	the	DET
ejpam-5846	48	14	drawing	drawing	NOUN
ejpam-5846	48	15	of	of	ADP
ejpam-5846	48	16	a	a	DET
ejpam-5846	48	17	given	give	VERB
ejpam-5846	48	18	problem	problem	NOUN
ejpam-5846	48	19	completely	completely	ADV
ejpam-5846	48	20	in	in	ADP
ejpam-5846	48	21	itself	itself	PRON
ejpam-5846	48	22	.	.	PUNCT
ejpam-5846	49	1	situation	situation	NOUN
ejpam-5846	49	2	4	4	NUM
ejpam-5846	49	3	.	.	X
ejpam-5846	49	4	equilateral	equilateral	ADJ
ejpam-5846	49	5	triangle	triangle	NOUN
ejpam-5846	49	6	can	can	AUX
ejpam-5846	49	7	be	be	AUX
ejpam-5846	49	8	constructed	construct	VERB
ejpam-5846	49	9	in	in	ADP
ejpam-5846	49	10	the	the	DET
ejpam-5846	49	11	internal	internal	ADJ
ejpam-5846	49	12	and	and	CCONJ
ejpam-5846	49	13	external	external	ADJ
ejpam-5846	49	14	domain	domain	NOUN
ejpam-5846	49	15	of	of	ADP
ejpam-5846	49	16	a	a	DET
ejpam-5846	49	17	given	give	VERB
ejpam-5846	49	18	problem	problem	NOUN
ejpam-5846	49	19	.	.	PUNCT
ejpam-5846	50	1	now	now	ADV
ejpam-5846	50	2	,	,	PUNCT
ejpam-5846	50	3	we	we	PRON
ejpam-5846	50	4	will	will	AUX
ejpam-5846	50	5	consider	consider	VERB
ejpam-5846	50	6	all	all	DET
ejpam-5846	50	7	the	the	DET
ejpam-5846	50	8	above	above	ADJ
ejpam-5846	50	9	cases	case	NOUN
ejpam-5846	50	10	in	in	ADP
ejpam-5846	50	11	solving	solve	VERB
ejpam-5846	50	12	specific	specific	ADJ
ejpam-5846	50	13	problems	problem	NOUN
ejpam-5846	50	14	.	.	PUNCT
ejpam-5846	51	1	first	first	ADV
ejpam-5846	51	2	,	,	PUNCT
ejpam-5846	51	3	we	we	PRON
ejpam-5846	51	4	implement	implement	VERB
ejpam-5846	51	5	situation	situation	NOUN
ejpam-5846	51	6	1	1	NUM
ejpam-5846	51	7	in	in	ADP
ejpam-5846	51	8	solving	solve	VERB
ejpam-5846	51	9	the	the	DET
ejpam-5846	51	10	following	follow	VERB
ejpam-5846	51	11	problem	problem	NOUN
ejpam-5846	51	12	.	.	PUNCT
ejpam-5846	52	1	problem	problem	NOUN
ejpam-5846	52	2	1	1	NUM
ejpam-5846	52	3	.	.	PUNCT
ejpam-5846	53	1	in	in	ADP
ejpam-5846	53	2	triangle	triangle	PROPN
ejpam-5846	53	3	abc	abc	PROPN
ejpam-5846	53	4	ab	ab	PROPN
ejpam-5846	53	5	=	=	PUNCT
ejpam-5846	53	6	ac	ac	PROPN
ejpam-5846	53	7	and	and	CCONJ
ejpam-5846	53	8	∠bac	∠bac	PROPN
ejpam-5846	53	9	=	=	PROPN
ejpam-5846	53	10	80	80	NUM
ejpam-5846	53	11	◦	◦	NOUN
ejpam-5846	53	12	.	.	PUNCT
ejpam-5846	54	1	let	let	VERB
ejpam-5846	54	2	d	d	NOUN
ejpam-5846	54	3	the	the	DET
ejpam-5846	54	4	interior	interior	ADJ
ejpam-5846	54	5	point	point	NOUN
ejpam-5846	54	6	of	of	ADP
ejpam-5846	54	7	this	this	DET
ejpam-5846	54	8	triangle	triangle	NOUN
ejpam-5846	54	9	.	.	PUNCT
ejpam-5846	55	1	if	if	SCONJ
ejpam-5846	55	2	∠abd	∠abd	NOUN
ejpam-5846	55	3	=	=	SYM
ejpam-5846	55	4	∠bad	∠bad	PROPN
ejpam-5846	55	5	=	=	SYM
ejpam-5846	55	6	10	10	NUM
ejpam-5846	55	7	◦	◦	NOUN
ejpam-5846	55	8	,	,	PUNCT
ejpam-5846	55	9	then	then	ADV
ejpam-5846	55	10	find	find	VERB
ejpam-5846	55	11	∠bdc	∠bdc	PRON
ejpam-5846	55	12	.	.	PUNCT
ejpam-5846	56	1	(	(	PUNCT
ejpam-5846	56	2	fig.1	fig.1	PROPN
ejpam-5846	56	3	.	.	PUNCT
ejpam-5846	56	4	)	)	PUNCT
ejpam-5846	57	1	first	first	ADV
ejpam-5846	57	2	,	,	PUNCT
ejpam-5846	57	3	we	we	PRON
ejpam-5846	57	4	will	will	AUX
ejpam-5846	57	5	show	show	VERB
ejpam-5846	57	6	the	the	DET
ejpam-5846	57	7	solution	solution	NOUN
ejpam-5846	57	8	to	to	ADP
ejpam-5846	57	9	the	the	DET
ejpam-5846	57	10	problem	problem	NOUN
ejpam-5846	57	11	using	use	VERB
ejpam-5846	57	12	the	the	DET
ejpam-5846	57	13	algebraic	algebraic	ADJ
ejpam-5846	57	14	method	method	NOUN
ejpam-5846	57	15	,	,	PUNCT
ejpam-5846	57	16	given	give	VERB
ejpam-5846	57	17	in	in	ADP
ejpam-5846	57	18	work	work	NOUN
ejpam-5846	57	19	[	[	X
ejpam-5846	57	20	11	11	NUM
ejpam-5846	57	21	,	,	PUNCT
ejpam-5846	57	22	p.	p.	NOUN
ejpam-5846	57	23	123	123	NUM
ejpam-5846	57	24	]	]	PUNCT
ejpam-5846	57	25	.	.	PUNCT
ejpam-5846	58	1	let	let	VERB
ejpam-5846	58	2	us	we	PRON
ejpam-5846	58	3	denote	denote	VERB
ejpam-5846	58	4	∠bdc	∠bdc	PUNCT
ejpam-5846	58	5	=	=	PUNCT
ejpam-5846	58	6	x	x	X
ejpam-5846	58	7	.	.	PUNCT
ejpam-5846	59	1	if	if	SCONJ
ejpam-5846	59	2	we	we	PRON
ejpam-5846	59	3	apply	apply	VERB
ejpam-5846	59	4	the	the	DET
ejpam-5846	59	5	sine	sine	NOUN
ejpam-5846	59	6	theorem	theorem	VERB
ejpam-5846	59	7	to	to	ADP
ejpam-5846	59	8	triangles	triangle	NOUN
ejpam-5846	59	9	adc	adc	PROPN
ejpam-5846	59	10	and	and	CCONJ
ejpam-5846	59	11	abd	abd	PROPN
ejpam-5846	59	12	,	,	PUNCT
ejpam-5846	59	13	respectively	respectively	ADV
ejpam-5846	59	14	,	,	PUNCT
ejpam-5846	59	15	we	we	PRON
ejpam-5846	59	16	get	get	VERB
ejpam-5846	59	17	:	:	PUNCT
ejpam-5846	59	18	ad	ad	NOUN
ejpam-5846	59	19	sin	sin	NOUN
ejpam-5846	59	20	(	(	PUNCT
ejpam-5846	59	21	x−	x−	PROPN
ejpam-5846	59	22	90	90	NUM
ejpam-5846	59	23	◦	◦	NOUN
ejpam-5846	59	24	)	)	PUNCT
ejpam-5846	59	25	=	=	SYM
ejpam-5846	59	26	ac	ac	PROPN
ejpam-5846	59	27	sin	sin	NOUN
ejpam-5846	59	28	(	(	PUNCT
ejpam-5846	59	29	200	200	NUM
ejpam-5846	59	30	◦	◦	NOUN
ejpam-5846	59	31	−	−	NOUN
ejpam-5846	59	32	x	x	NOUN
ejpam-5846	59	33	)	)	PUNCT
ejpam-5846	59	34	,	,	PUNCT
ejpam-5846	59	35	ad	ad	NOUN
ejpam-5846	59	36	sin	sin	NOUN
ejpam-5846	59	37	10	10	NUM
ejpam-5846	59	38	◦	◦	NOUN
ejpam-5846	59	39	=	=	SYM
ejpam-5846	59	40	ab	ab	PROPN
ejpam-5846	59	41	sin	sin	NOUN
ejpam-5846	59	42	160	160	NUM
ejpam-5846	59	43	◦	◦	NOUN
ejpam-5846	59	44	.	.	PUNCT
ejpam-5846	60	1	considering	consider	VERB
ejpam-5846	60	2	the	the	DET
ejpam-5846	60	3	relation	relation	NOUN
ejpam-5846	60	4	ab	ab	PROPN
ejpam-5846	60	5	=	=	PUNCT
ejpam-5846	60	6	ac	ac	PROPN
ejpam-5846	60	7	,	,	PUNCT
ejpam-5846	60	8	if	if	SCONJ
ejpam-5846	60	9	we	we	PRON
ejpam-5846	60	10	divide	divide	VERB
ejpam-5846	60	11	the	the	DET
ejpam-5846	60	12	two	two	NUM
ejpam-5846	60	13	above	above	ADJ
ejpam-5846	60	14	equalities	equality	NOUN
ejpam-5846	60	15	term	term	NOUN
ejpam-5846	60	16	by	by	ADP
ejpam-5846	60	17	term	term	NOUN
ejpam-5846	60	18	,	,	PUNCT
ejpam-5846	60	19	we	we	PRON
ejpam-5846	60	20	get	get	AUX
ejpam-5846	60	21	:	:	PUNCT
ejpam-5846	60	22	sin	sin	NOUN
ejpam-5846	60	23	10	10	NUM
ejpam-5846	60	24	◦	◦	NOUN
ejpam-5846	60	25	sin	sin	NOUN
ejpam-5846	60	26	(	(	PUNCT
ejpam-5846	60	27	x−	x−	PROPN
ejpam-5846	60	28	90	90	NUM
ejpam-5846	60	29	◦	◦	NOUN
ejpam-5846	60	30	)	)	PUNCT
ejpam-5846	60	31	=	=	PRON
ejpam-5846	60	32	sin	sin	VERB
ejpam-5846	60	33	160	160	NUM
ejpam-5846	60	34	◦	◦	NOUN
ejpam-5846	60	35	sin	sin	NOUN
ejpam-5846	60	36	(	(	PUNCT
ejpam-5846	60	37	200	200	NUM
ejpam-5846	60	38	◦	◦	NOUN
ejpam-5846	60	39	−	−	NOUN
ejpam-5846	60	40	x	x	NOUN
ejpam-5846	60	41	)	)	PUNCT
ejpam-5846	60	42	or	or	CCONJ
ejpam-5846	60	43	sin	sin	VERB
ejpam-5846	60	44	160	160	NUM
ejpam-5846	60	45	◦	◦	NOUN
ejpam-5846	60	46	·	·	PUNCT
ejpam-5846	60	47	sin	sin	NOUN
ejpam-5846	60	48	(	(	PUNCT
ejpam-5846	60	49	x−	x−	PROPN
ejpam-5846	60	50	90	90	NUM
ejpam-5846	60	51	◦	◦	NOUN
ejpam-5846	60	52	)	)	PUNCT
ejpam-5846	60	53	=	=	PRON
ejpam-5846	60	54	sin	sin	NOUN
ejpam-5846	60	55	10	10	NUM
ejpam-5846	60	56	◦	◦	NOUN
ejpam-5846	60	57	·	·	PUNCT
ejpam-5846	60	58	sin	sin	NOUN
ejpam-5846	60	59	(	(	PUNCT
ejpam-5846	60	60	200	200	NUM
ejpam-5846	60	61	◦	◦	NOUN
ejpam-5846	60	62	−	−	NOUN
ejpam-5846	60	63	x	x	NOUN
ejpam-5846	60	64	)	)	PUNCT
ejpam-5846	60	65	.	.	PUNCT
ejpam-5846	61	1	to	to	PART
ejpam-5846	61	2	find	find	VERB
ejpam-5846	61	3	x	x	PRON
ejpam-5846	61	4	from	from	ADP
ejpam-5846	61	5	the	the	DET
ejpam-5846	61	6	last	last	ADJ
ejpam-5846	61	7	relation	relation	NOUN
ejpam-5846	61	8	,	,	PUNCT
ejpam-5846	61	9	let	let	VERB
ejpam-5846	61	10	us	we	PRON
ejpam-5846	61	11	perform	perform	VERB
ejpam-5846	61	12	the	the	DET
ejpam-5846	61	13	following	follow	VERB
ejpam-5846	61	14	transformations	transformation	NOUN
ejpam-5846	61	15	:	:	PUNCT
ejpam-5846	61	16	sin	sin	NOUN
ejpam-5846	61	17	20	20	NUM
ejpam-5846	61	18	◦	◦	NOUN
ejpam-5846	61	19	·	·	PUNCT
ejpam-5846	61	20	sin	sin	NOUN
ejpam-5846	61	21	(	(	PUNCT
ejpam-5846	61	22	x−	x−	PROPN
ejpam-5846	61	23	90	90	NUM
ejpam-5846	61	24	◦	◦	NOUN
ejpam-5846	61	25	)	)	PUNCT
ejpam-5846	61	26	=	=	PRON
ejpam-5846	61	27	sin	sin	NOUN
ejpam-5846	61	28	10	10	NUM
ejpam-5846	61	29	◦	◦	NOUN
ejpam-5846	61	30	·	·	PUNCT
ejpam-5846	61	31	sin	sin	NOUN
ejpam-5846	61	32	(	(	PUNCT
ejpam-5846	61	33	200	200	NUM
ejpam-5846	61	34	◦	◦	NOUN
ejpam-5846	61	35	−	−	NOUN
ejpam-5846	61	36	x	x	NOUN
ejpam-5846	61	37	)	)	PUNCT
ejpam-5846	61	38	,	,	PUNCT
ejpam-5846	61	39	s.	s.	PROPN
ejpam-5846	61	40	j.	j.	PROPN
ejpam-5846	61	41	aliyev	aliyev	PROPN
ejpam-5846	61	42	,	,	PUNCT
ejpam-5846	61	43	m.	m.	PROPN
ejpam-5846	61	44	n.	n.	PROPN
ejpam-5846	61	45	heydarova	heydarova	PROPN
ejpam-5846	61	46	,	,	PUNCT
ejpam-5846	61	47	a.	a.	NOUN
ejpam-5846	61	48	m.	m.	PROPN
ejpam-5846	61	49	seyidova	seyidova	PROPN
ejpam-5846	61	50	/	/	SYM
ejpam-5846	61	51	eur	eur	PROPN
ejpam-5846	61	52	.	.	PUNCT
ejpam-5846	62	1	j.	j.	PROPN
ejpam-5846	62	2	pure	pure	PROPN
ejpam-5846	62	3	appl	appl	PROPN
ejpam-5846	62	4	.	.	PROPN
ejpam-5846	62	5	math	math	PROPN
ejpam-5846	62	6	,	,	PUNCT
ejpam-5846	62	7	18	18	NUM
ejpam-5846	62	8	(	(	PUNCT
ejpam-5846	62	9	1	1	NUM
ejpam-5846	62	10	)	)	PUNCT
ejpam-5846	62	11	(	(	PUNCT
ejpam-5846	62	12	2025	2025	NUM
ejpam-5846	62	13	)	)	PUNCT
ejpam-5846	62	14	,	,	PUNCT
ejpam-5846	62	15	5846	5846	NUM
ejpam-5846	62	16	4	4	NUM
ejpam-5846	62	17	of	of	ADP
ejpam-5846	62	18	9	9	NUM
ejpam-5846	62	19	figure	figure	NOUN
ejpam-5846	62	20	1	1	NUM
ejpam-5846	62	21	:	:	PUNCT
ejpam-5846	62	22	(	(	PUNCT
ejpam-5846	62	23	isosceles	isoscele	NOUN
ejpam-5846	62	24	triangle	triangle	VERB
ejpam-5846	62	25	abc	abc	PROPN
ejpam-5846	62	26	with	with	ADP
ejpam-5846	62	27	the	the	DET
ejpam-5846	62	28	given	give	VERB
ejpam-5846	62	29	angles	angle	NOUN
ejpam-5846	62	30	)	)	PUNCT
ejpam-5846	62	31	figure	figure	NOUN
ejpam-5846	62	32	2	2	NUM
ejpam-5846	62	33	:	:	PUNCT
ejpam-5846	62	34	(	(	PUNCT
ejpam-5846	62	35	triangle	triangle	NOUN
ejpam-5846	62	36	ade	ade	NOUN
ejpam-5846	62	37	is	be	AUX
ejpam-5846	62	38	equilateral	equilateral	ADJ
ejpam-5846	62	39	,	,	PUNCT
ejpam-5846	62	40	constructed	construct	VERB
ejpam-5846	62	41	inside	inside	ADP
ejpam-5846	62	42	the	the	DET
ejpam-5846	62	43	triangle	triangle	NOUN
ejpam-5846	62	44	abc	abc	PROPN
ejpam-5846	62	45	)	)	PUNCT
ejpam-5846	62	46	2	2	NUM
ejpam-5846	62	47	·	·	PUNCT
ejpam-5846	62	48	sin	sin	NOUN
ejpam-5846	62	49	10	10	NUM
ejpam-5846	62	50	◦	◦	NOUN
ejpam-5846	62	51	cos	cos	PROPN
ejpam-5846	62	52	10	10	NUM
ejpam-5846	62	53	◦	◦	NOUN
ejpam-5846	62	54	·	·	PUNCT
ejpam-5846	62	55	sin	sin	NOUN
ejpam-5846	62	56	(	(	PUNCT
ejpam-5846	62	57	x−	x−	PROPN
ejpam-5846	62	58	90	90	NUM
ejpam-5846	62	59	◦	◦	NOUN
ejpam-5846	62	60	)	)	PUNCT
ejpam-5846	62	61	=	=	PRON
ejpam-5846	62	62	sin	sin	NOUN
ejpam-5846	62	63	10	10	NUM
ejpam-5846	62	64	◦	◦	NOUN
ejpam-5846	62	65	·	·	PUNCT
ejpam-5846	62	66	sin	sin	NOUN
ejpam-5846	62	67	(	(	PUNCT
ejpam-5846	62	68	200	200	NUM
ejpam-5846	62	69	◦	◦	NOUN
ejpam-5846	62	70	−	−	NOUN
ejpam-5846	62	71	x	x	NOUN
ejpam-5846	62	72	)	)	PUNCT
ejpam-5846	62	73	,	,	PUNCT
ejpam-5846	62	74	cos	cos	ADP
ejpam-5846	62	75	10	10	NUM
ejpam-5846	62	76	◦	◦	NOUN
ejpam-5846	62	77	·	·	PUNCT
ejpam-5846	62	78	sin	sin	NOUN
ejpam-5846	62	79	(	(	PUNCT
ejpam-5846	62	80	x−	x−	PROPN
ejpam-5846	62	81	90	90	NUM
ejpam-5846	62	82	◦	◦	NOUN
ejpam-5846	62	83	)	)	PUNCT
ejpam-5846	62	84	=	=	SYM
ejpam-5846	63	1	cos	cos	ADP
ejpam-5846	63	2	60	60	NUM
ejpam-5846	63	3	◦	◦	NOUN
ejpam-5846	63	4	·	·	PUNCT
ejpam-5846	63	5	sin	sin	NOUN
ejpam-5846	63	6	(	(	PUNCT
ejpam-5846	63	7	200	200	NUM
ejpam-5846	63	8	◦	◦	NOUN
ejpam-5846	63	9	−	−	NOUN
ejpam-5846	63	10	x	x	NOUN
ejpam-5846	63	11	)	)	PUNCT
ejpam-5846	63	12	,	,	PUNCT
ejpam-5846	63	13	1	1	NUM
ejpam-5846	63	14	2	2	NUM
ejpam-5846	63	15	·	·	PUNCT
ejpam-5846	64	1	[	[	X
ejpam-5846	64	2	sin	sin	X
ejpam-5846	64	3	(	(	PUNCT
ejpam-5846	64	4	x−	x−	PROPN
ejpam-5846	64	5	80	80	NUM
ejpam-5846	64	6	◦	◦	NOUN
ejpam-5846	64	7	)	)	PUNCT
ejpam-5846	64	8	+	+	CCONJ
ejpam-5846	64	9	sin	sin	NOUN
ejpam-5846	64	10	(	(	PUNCT
ejpam-5846	64	11	100	100	NUM
ejpam-5846	64	12	◦	◦	NOUN
ejpam-5846	64	13	−	−	NUM
ejpam-5846	64	14	x	x	NOUN
ejpam-5846	64	15	)	)	PUNCT
ejpam-5846	64	16	]	]	PUNCT
ejpam-5846	64	17	=	=	SYM
ejpam-5846	64	18	1	1	NUM
ejpam-5846	64	19	2	2	NUM
ejpam-5846	64	20	·	·	PUNCT
ejpam-5846	65	1	[	[	X
ejpam-5846	65	2	sin	sin	NOUN
ejpam-5846	65	3	(	(	PUNCT
ejpam-5846	65	4	260	260	NUM
ejpam-5846	65	5	◦	◦	NOUN
ejpam-5846	65	6	−	−	NOUN
ejpam-5846	65	7	x	x	NOUN
ejpam-5846	65	8	)	)	PUNCT
ejpam-5846	65	9	+	+	CCONJ
ejpam-5846	65	10	sin	sin	NOUN
ejpam-5846	65	11	(	(	PUNCT
ejpam-5846	65	12	x−	x−	PROPN
ejpam-5846	65	13	140	140	NUM
ejpam-5846	65	14	◦	◦	NOUN
ejpam-5846	65	15	)	)	PUNCT
ejpam-5846	65	16	]	]	PUNCT
ejpam-5846	65	17	.	.	PUNCT
ejpam-5846	66	1	note	note	VERB
ejpam-5846	66	2	that	that	DET
ejpam-5846	66	3	sin	sin	NOUN
ejpam-5846	66	4	(	(	PUNCT
ejpam-5846	66	5	x−	x−	PROPN
ejpam-5846	66	6	80	80	NUM
ejpam-5846	66	7	◦	◦	NOUN
ejpam-5846	66	8	)	)	PUNCT
ejpam-5846	66	9	=	=	VERB
ejpam-5846	66	10	sin	sin	NOUN
ejpam-5846	66	11	(	(	PUNCT
ejpam-5846	66	12	260	260	NUM
ejpam-5846	66	13	◦	◦	NOUN
ejpam-5846	66	14	−	−	NOUN
ejpam-5846	66	15	x	x	NOUN
ejpam-5846	66	16	)	)	PUNCT
ejpam-5846	66	17	,	,	PUNCT
ejpam-5846	66	18	because	because	SCONJ
ejpam-5846	66	19	(	(	PUNCT
ejpam-5846	66	20	x−	x−	PROPN
ejpam-5846	66	21	80	80	NUM
ejpam-5846	66	22	◦	◦	NOUN
ejpam-5846	66	23	)	)	PUNCT
ejpam-5846	66	24	+	+	CCONJ
ejpam-5846	66	25	(	(	PUNCT
ejpam-5846	66	26	260	260	NUM
ejpam-5846	66	27	◦	◦	NOUN
ejpam-5846	66	28	−	−	NOUN
ejpam-5846	66	29	x	x	NOUN
ejpam-5846	66	30	)	)	PUNCT
ejpam-5846	66	31	=	=	NOUN
ejpam-5846	66	32	180	180	NUM
ejpam-5846	66	33	◦	◦	NOUN
ejpam-5846	66	34	.	.	PUNCT
ejpam-5846	67	1	then	then	ADV
ejpam-5846	67	2	,	,	PUNCT
ejpam-5846	67	3	from	from	ADP
ejpam-5846	67	4	the	the	DET
ejpam-5846	67	5	last	last	ADJ
ejpam-5846	67	6	relation	relation	NOUN
ejpam-5846	67	7	,	,	PUNCT
ejpam-5846	67	8	we	we	PRON
ejpam-5846	67	9	find	find	VERB
ejpam-5846	67	10	sin	sin	NOUN
ejpam-5846	67	11	(	(	PUNCT
ejpam-5846	67	12	100	100	NUM
ejpam-5846	67	13	◦	◦	NOUN
ejpam-5846	67	14	−	−	NUM
ejpam-5846	67	15	x	x	NOUN
ejpam-5846	67	16	)	)	PUNCT
ejpam-5846	67	17	=	=	VERB
ejpam-5846	67	18	sin	sin	NOUN
ejpam-5846	67	19	(	(	PUNCT
ejpam-5846	67	20	x−	x−	PROPN
ejpam-5846	67	21	140	140	NUM
ejpam-5846	67	22	◦	◦	NOUN
ejpam-5846	67	23	)	)	PUNCT
ejpam-5846	67	24	,	,	PUNCT
ejpam-5846	67	25	100	100	NUM
ejpam-5846	67	26	◦	◦	NOUN
ejpam-5846	67	27	−	−	NOUN
ejpam-5846	67	28	x	x	SYM
ejpam-5846	68	1	=	=	SYM
ejpam-5846	68	2	x−	x−	PROPN
ejpam-5846	68	3	140	140	NUM
ejpam-5846	68	4	◦	◦	NOUN
ejpam-5846	68	5	,⇒	,⇒	NOUN
ejpam-5846	68	6	x	x	X
ejpam-5846	68	7	=	=	SYM
ejpam-5846	68	8	120	120	NUM
ejpam-5846	68	9	◦	◦	NOUN
ejpam-5846	68	10	.	.	PUNCT
ejpam-5846	69	1	now	now	ADV
ejpam-5846	69	2	,	,	PUNCT
ejpam-5846	69	3	let	let	VERB
ejpam-5846	69	4	us	we	PRON
ejpam-5846	69	5	solve	solve	VERB
ejpam-5846	69	6	the	the	DET
ejpam-5846	69	7	given	give	VERB
ejpam-5846	69	8	problem	problem	NOUN
ejpam-5846	69	9	using	use	VERB
ejpam-5846	69	10	a	a	DET
ejpam-5846	69	11	purely	purely	ADV
ejpam-5846	69	12	geometric	geometric	ADJ
ejpam-5846	69	13	method	method	NOUN
ejpam-5846	69	14	(	(	PUNCT
ejpam-5846	69	15	by	by	ADP
ejpam-5846	69	16	including	include	VERB
ejpam-5846	69	17	an	an	DET
ejpam-5846	69	18	equilateral	equilateral	ADJ
ejpam-5846	69	19	triangle	triangle	NOUN
ejpam-5846	69	20	)	)	PUNCT
ejpam-5846	69	21	.	.	PUNCT
ejpam-5846	70	1	since	since	SCONJ
ejpam-5846	70	2	the	the	DET
ejpam-5846	70	3	angle	angle	NOUN
ejpam-5846	70	4	at	at	ADP
ejpam-5846	70	5	the	the	DET
ejpam-5846	70	6	vertex	vertex	NOUN
ejpam-5846	70	7	∠bac	∠bac	PROPN
ejpam-5846	70	8	=	=	PROPN
ejpam-5846	70	9	80	80	NUM
ejpam-5846	70	10	◦	◦	NOUN
ejpam-5846	70	11	,	,	PUNCT
ejpam-5846	70	12	then	then	ADV
ejpam-5846	70	13	inside	inside	ADP
ejpam-5846	70	14	the	the	DET
ejpam-5846	70	15	triangle	triangle	NOUN
ejpam-5846	70	16	abc	abc	PROPN
ejpam-5846	70	17	can	can	AUX
ejpam-5846	70	18	be	be	AUX
ejpam-5846	70	19	construct	construct	VERB
ejpam-5846	70	20	an	an	DET
ejpam-5846	70	21	equilateral	equilateral	ADJ
ejpam-5846	70	22	triangle	triangle	NOUN
ejpam-5846	70	23	.	.	PUNCT
ejpam-5846	71	1	to	to	ADP
ejpam-5846	71	2	this	this	DET
ejpam-5846	71	3	end	end	NOUN
ejpam-5846	71	4	,	,	PUNCT
ejpam-5846	71	5	we	we	PRON
ejpam-5846	71	6	construct	construct	VERB
ejpam-5846	71	7	triangle	triangle	NOUN
ejpam-5846	71	8	aec	aec	PROPN
ejpam-5846	71	9	on	on	ADP
ejpam-5846	71	10	side	side	NOUN
ejpam-5846	71	11	ac	ac	PROPN
ejpam-5846	71	12	,	,	PUNCT
ejpam-5846	71	13	which	which	PRON
ejpam-5846	71	14	is	be	AUX
ejpam-5846	71	15	equal	equal	ADJ
ejpam-5846	71	16	to	to	PART
ejpam-5846	71	17	triangle	triangle	VERB
ejpam-5846	71	18	adb	adb	NOUN
ejpam-5846	71	19	.	.	PUNCT
ejpam-5846	72	1	connecting	connect	VERB
ejpam-5846	72	2	points	point	NOUN
ejpam-5846	72	3	d	d	NOUN
ejpam-5846	72	4	and	and	CCONJ
ejpam-5846	72	5	e	e	NOUN
ejpam-5846	72	6	,	,	PUNCT
ejpam-5846	72	7	taking	take	VERB
ejpam-5846	72	8	into	into	ADP
ejpam-5846	72	9	account	account	NOUN
ejpam-5846	72	10	ad	ad	NOUN
ejpam-5846	72	11	=	=	SYM
ejpam-5846	72	12	ae	ae	PROPN
ejpam-5846	72	13	,	,	PUNCT
ejpam-5846	72	14	we	we	PRON
ejpam-5846	72	15	get	get	VERB
ejpam-5846	72	16	an	an	DET
ejpam-5846	72	17	equilateral	equilateral	ADJ
ejpam-5846	72	18	triangle	triangle	NOUN
ejpam-5846	72	19	ade	ade	NOUN
ejpam-5846	72	20	.	.	PUNCT
ejpam-5846	73	1	as	as	ADP
ejpam-5846	73	2	the	the	DET
ejpam-5846	73	3	de	de	X
ejpam-5846	73	4	=	=	PROPN
ejpam-5846	73	5	ec	ec	PROPN
ejpam-5846	73	6	,	,	PUNCT
ejpam-5846	73	7	then	then	ADV
ejpam-5846	73	8	the	the	DET
ejpam-5846	73	9	triangle	triangle	NOUN
ejpam-5846	73	10	dec	dec	PROPN
ejpam-5846	73	11	is	be	AUX
ejpam-5846	73	12	isosceles	isoscele	NOUN
ejpam-5846	73	13	and	and	CCONJ
ejpam-5846	73	14	∠edc	∠edc	NOUN
ejpam-5846	73	15	=	=	SYM
ejpam-5846	74	1	∠ecd	∠ecd	PROPN
ejpam-5846	74	2	=	=	PUNCT
ejpam-5846	74	3	20	20	NUM
ejpam-5846	74	4	◦	◦	NOUN
ejpam-5846	74	5	.	.	PUNCT
ejpam-5846	75	1	s.	s.	PROPN
ejpam-5846	75	2	j.	j.	PROPN
ejpam-5846	75	3	aliyev	aliyev	PROPN
ejpam-5846	75	4	,	,	PUNCT
ejpam-5846	75	5	m.	m.	PROPN
ejpam-5846	75	6	n.	n.	PROPN
ejpam-5846	75	7	heydarova	heydarova	PROPN
ejpam-5846	75	8	,	,	PUNCT
ejpam-5846	75	9	a.	a.	NOUN
ejpam-5846	75	10	m.	m.	PROPN
ejpam-5846	75	11	seyidova	seyidova	PROPN
ejpam-5846	75	12	/	/	SYM
ejpam-5846	75	13	eur	eur	PROPN
ejpam-5846	75	14	.	.	PUNCT
ejpam-5846	76	1	j.	j.	PROPN
ejpam-5846	76	2	pure	pure	PROPN
ejpam-5846	76	3	appl	appl	PROPN
ejpam-5846	76	4	.	.	PROPN
ejpam-5846	76	5	math	math	PROPN
ejpam-5846	76	6	,	,	PUNCT
ejpam-5846	76	7	18	18	NUM
ejpam-5846	76	8	(	(	PUNCT
ejpam-5846	76	9	1	1	NUM
ejpam-5846	76	10	)	)	PUNCT
ejpam-5846	76	11	(	(	PUNCT
ejpam-5846	76	12	2025	2025	NUM
ejpam-5846	76	13	)	)	PUNCT
ejpam-5846	76	14	,	,	PUNCT
ejpam-5846	76	15	5846	5846	NUM
ejpam-5846	76	16	5	5	NUM
ejpam-5846	76	17	of	of	ADP
ejpam-5846	76	18	9	9	NUM
ejpam-5846	76	19	figure	figure	NOUN
ejpam-5846	76	20	3	3	NUM
ejpam-5846	76	21	:	:	PUNCT
ejpam-5846	76	22	(	(	PUNCT
ejpam-5846	76	23	abd	abd	PROPN
ejpam-5846	76	24	is	be	AUX
ejpam-5846	76	25	a	a	DET
ejpam-5846	76	26	given	give	VERB
ejpam-5846	76	27	triangle	triangle	NOUN
ejpam-5846	76	28	and	and	CCONJ
ejpam-5846	76	29	triangle	triangle	NOUN
ejpam-5846	76	30	abc	abc	PROPN
ejpam-5846	76	31	is	be	AUX
ejpam-5846	76	32	isosceles	isoscele	NOUN
ejpam-5846	76	33	)	)	PUNCT
ejpam-5846	76	34	figure	figure	NOUN
ejpam-5846	76	35	4	4	NUM
ejpam-5846	76	36	:	:	PUNCT
ejpam-5846	76	37	(	(	PUNCT
ejpam-5846	76	38	triangle	triangle	NOUN
ejpam-5846	76	39	bce	bce	PROPN
ejpam-5846	76	40	is	be	AUX
ejpam-5846	76	41	equilateral	equilateral	ADJ
ejpam-5846	76	42	,	,	PUNCT
ejpam-5846	76	43	constructed	construct	VERB
ejpam-5846	76	44	outside	outside	ADP
ejpam-5846	76	45	the	the	DET
ejpam-5846	76	46	triangle	triangle	NOUN
ejpam-5846	76	47	abd	abd	PROPN
ejpam-5846	76	48	)	)	PUNCT
ejpam-5846	76	49	since	since	SCONJ
ejpam-5846	76	50	the	the	DET
ejpam-5846	76	51	adjacent	adjacent	ADJ
ejpam-5846	76	52	angles	angle	NOUN
ejpam-5846	76	53	at	at	ADP
ejpam-5846	76	54	the	the	DET
ejpam-5846	76	55	base	base	NOUN
ejpam-5846	76	56	of	of	ADP
ejpam-5846	76	57	triangle	triangle	NOUN
ejpam-5846	76	58	abc	abc	PROPN
ejpam-5846	76	59	are	be	AUX
ejpam-5846	76	60	equal	equal	ADJ
ejpam-5846	76	61	to	to	ADP
ejpam-5846	76	62	50	50	NUM
ejpam-5846	76	63	◦	◦	NOUN
ejpam-5846	76	64	,	,	PUNCT
ejpam-5846	76	65	then	then	ADV
ejpam-5846	76	66	in	in	ADP
ejpam-5846	76	67	the	the	DET
ejpam-5846	76	68	triangle	triangle	NOUN
ejpam-5846	76	69	bdc	bdc	NOUN
ejpam-5846	76	70	,	,	PUNCT
ejpam-5846	76	71	we	we	PRON
ejpam-5846	76	72	find	find	VERB
ejpam-5846	76	73	∠bdc	∠bdc	PRON
ejpam-5846	76	74	=	=	SYM
ejpam-5846	76	75	180	180	NUM
ejpam-5846	76	76	◦	◦	NOUN
ejpam-5846	76	77	−	−	PROPN
ejpam-5846	76	78	(	(	PUNCT
ejpam-5846	76	79	40	40	NUM
ejpam-5846	76	80	◦	◦	NOUN
ejpam-5846	76	81	+	+	CCONJ
ejpam-5846	76	82	20	20	NUM
ejpam-5846	76	83	◦	◦	NOUN
ejpam-5846	76	84	)	)	PUNCT
ejpam-5846	76	85	=	=	SYM
ejpam-5846	76	86	120	120	NUM
ejpam-5846	76	87	◦	◦	NOUN
ejpam-5846	76	88	.	.	PUNCT
ejpam-5846	77	1	(	(	PUNCT
ejpam-5846	77	2	fig.2	fig.2	PROPN
ejpam-5846	77	3	.	.	PUNCT
ejpam-5846	77	4	)	)	PUNCT
ejpam-5846	78	1	the	the	DET
ejpam-5846	78	2	comparison	comparison	NOUN
ejpam-5846	78	3	of	of	ADP
ejpam-5846	78	4	these	these	DET
ejpam-5846	78	5	two	two	NUM
ejpam-5846	78	6	methods	method	NOUN
ejpam-5846	78	7	show	show	VERB
ejpam-5846	78	8	that	that	SCONJ
ejpam-5846	78	9	,	,	PUNCT
ejpam-5846	78	10	although	although	SCONJ
ejpam-5846	78	11	the	the	DET
ejpam-5846	78	12	introduction	introduction	NOUN
ejpam-5846	78	13	of	of	ADP
ejpam-5846	78	14	an	an	DET
ejpam-5846	78	15	equilateral	equilateral	ADJ
ejpam-5846	78	16	triangle	triangle	NOUN
ejpam-5846	78	17	may	may	AUX
ejpam-5846	78	18	seem	seem	VERB
ejpam-5846	78	19	difficult	difficult	ADJ
ejpam-5846	78	20	when	when	SCONJ
ejpam-5846	78	21	solving	solve	VERB
ejpam-5846	78	22	the	the	DET
ejpam-5846	78	23	problem	problem	NOUN
ejpam-5846	78	24	using	use	VERB
ejpam-5846	78	25	the	the	DET
ejpam-5846	78	26	second	second	ADJ
ejpam-5846	78	27	method	method	NOUN
ejpam-5846	78	28	(	(	PUNCT
ejpam-5846	78	29	this	this	PRON
ejpam-5846	78	30	may	may	AUX
ejpam-5846	78	31	not	not	PART
ejpam-5846	78	32	occur	occur	VERB
ejpam-5846	78	33	to	to	ADP
ejpam-5846	78	34	everyone	everyone	PRON
ejpam-5846	78	35	)	)	PUNCT
ejpam-5846	78	36	,	,	PUNCT
ejpam-5846	78	37	with	with	ADP
ejpam-5846	78	38	this	this	DET
ejpam-5846	78	39	method	method	NOUN
ejpam-5846	78	40	the	the	DET
ejpam-5846	78	41	answer	answer	NOUN
ejpam-5846	78	42	is	be	AUX
ejpam-5846	78	43	found	find	VERB
ejpam-5846	78	44	very	very	ADV
ejpam-5846	78	45	quickly	quickly	ADV
ejpam-5846	78	46	,	,	PUNCT
ejpam-5846	78	47	without	without	ADP
ejpam-5846	78	48	using	use	VERB
ejpam-5846	78	49	any	any	DET
ejpam-5846	78	50	formulas	formula	NOUN
ejpam-5846	78	51	or	or	CCONJ
ejpam-5846	78	52	theorems	theorem	NOUN
ejpam-5846	78	53	.	.	PUNCT
ejpam-5846	79	1	we	we	PRON
ejpam-5846	79	2	implement	implement	VERB
ejpam-5846	79	3	situation	situation	NOUN
ejpam-5846	79	4	2	2	NUM
ejpam-5846	79	5	in	in	ADP
ejpam-5846	79	6	solving	solve	VERB
ejpam-5846	79	7	the	the	DET
ejpam-5846	79	8	following	follow	VERB
ejpam-5846	79	9	problem	problem	NOUN
ejpam-5846	79	10	.	.	PUNCT
ejpam-5846	80	1	problem	problem	NOUN
ejpam-5846	80	2	2	2	NUM
ejpam-5846	80	3	.	.	PUNCT
ejpam-5846	81	1	the	the	DET
ejpam-5846	81	2	point	point	NOUN
ejpam-5846	81	3	c	c	NOUN
ejpam-5846	81	4	is	be	AUX
ejpam-5846	81	5	given	give	VERB
ejpam-5846	81	6	on	on	ADP
ejpam-5846	81	7	the	the	DET
ejpam-5846	81	8	side	side	NOUN
ejpam-5846	81	9	bd	bd	PROPN
ejpam-5846	81	10	of	of	ADP
ejpam-5846	81	11	the	the	DET
ejpam-5846	81	12	triangle	triangle	NOUN
ejpam-5846	81	13	abd	abd	PROPN
ejpam-5846	81	14	,	,	PUNCT
ejpam-5846	81	15	so	so	SCONJ
ejpam-5846	81	16	that	that	SCONJ
ejpam-5846	81	17	ab	ab	PROPN
ejpam-5846	81	18	=	=	SYM
ejpam-5846	81	19	bc	bc	PROPN
ejpam-5846	81	20	,	,	PUNCT
ejpam-5846	81	21	ac	ac	PROPN
ejpam-5846	82	1	=	=	SYM
ejpam-5846	82	2	bd	bd	PROPN
ejpam-5846	82	3	and	and	CCONJ
ejpam-5846	82	4	∠acb	∠acb	NOUN
ejpam-5846	82	5	=	=	SYM
ejpam-5846	82	6	40	40	NUM
ejpam-5846	82	7	◦	◦	NOUN
ejpam-5846	82	8	.	.	PUNCT
ejpam-5846	82	9	find	find	VERB
ejpam-5846	82	10	∠cad	∠cad	PROPN
ejpam-5846	82	11	.	.	PUNCT
ejpam-5846	83	1	(	(	PUNCT
ejpam-5846	83	2	fig.3	fig.3	PROPN
ejpam-5846	83	3	.	.	PUNCT
ejpam-5846	83	4	)	)	PUNCT
ejpam-5846	83	5	figure	figure	VERB
ejpam-5846	83	6	5	5	NUM
ejpam-5846	83	7	:	:	PUNCT
ejpam-5846	83	8	(	(	PUNCT
ejpam-5846	83	9	triangle	triangle	VERB
ejpam-5846	83	10	abc	abc	PROPN
ejpam-5846	83	11	with	with	ADP
ejpam-5846	83	12	the	the	DET
ejpam-5846	83	13	given	give	VERB
ejpam-5846	83	14	angles	angle	NOUN
ejpam-5846	83	15	)	)	PUNCT
ejpam-5846	83	16	s.	s.	PROPN
ejpam-5846	83	17	j.	j.	PROPN
ejpam-5846	83	18	aliyev	aliyev	PROPN
ejpam-5846	83	19	,	,	PUNCT
ejpam-5846	83	20	m.	m.	PROPN
ejpam-5846	83	21	n.	n.	PROPN
ejpam-5846	83	22	heydarova	heydarova	PROPN
ejpam-5846	83	23	,	,	PUNCT
ejpam-5846	83	24	a.	a.	NOUN
ejpam-5846	83	25	m.	m.	PROPN
ejpam-5846	83	26	seyidova	seyidova	PROPN
ejpam-5846	83	27	/	/	SYM
ejpam-5846	83	28	eur	eur	PROPN
ejpam-5846	83	29	.	.	PUNCT
ejpam-5846	84	1	j.	j.	PROPN
ejpam-5846	84	2	pure	pure	PROPN
ejpam-5846	84	3	appl	appl	PROPN
ejpam-5846	84	4	.	.	PROPN
ejpam-5846	84	5	math	math	PROPN
ejpam-5846	84	6	,	,	PUNCT
ejpam-5846	84	7	18	18	NUM
ejpam-5846	84	8	(	(	PUNCT
ejpam-5846	84	9	1	1	NUM
ejpam-5846	84	10	)	)	PUNCT
ejpam-5846	84	11	(	(	PUNCT
ejpam-5846	84	12	2025	2025	NUM
ejpam-5846	84	13	)	)	PUNCT
ejpam-5846	84	14	,	,	PUNCT
ejpam-5846	84	15	5846	5846	NUM
ejpam-5846	84	16	6	6	NUM
ejpam-5846	84	17	of	of	ADP
ejpam-5846	84	18	9	9	NUM
ejpam-5846	84	19	figure	figure	NOUN
ejpam-5846	84	20	6	6	NUM
ejpam-5846	84	21	:	:	PUNCT
ejpam-5846	84	22	(	(	PUNCT
ejpam-5846	84	23	given	give	VERB
ejpam-5846	84	24	triangle	triangle	PROPN
ejpam-5846	84	25	abc	abc	PROPN
ejpam-5846	84	26	,	,	PUNCT
ejpam-5846	84	27	placed	place	VERB
ejpam-5846	84	28	inside	inside	ADP
ejpam-5846	84	29	the	the	DET
ejpam-5846	84	30	equilateral	equilateral	ADJ
ejpam-5846	84	31	triangle	triangle	NOUN
ejpam-5846	84	32	bdc	bdc	NOUN
ejpam-5846	84	33	)	)	PUNCT
ejpam-5846	84	34	figure	figure	NOUN
ejpam-5846	84	35	7	7	NUM
ejpam-5846	84	36	:	:	PUNCT
ejpam-5846	84	37	(	(	PUNCT
ejpam-5846	84	38	triangle	triangle	VERB
ejpam-5846	84	39	abc	abc	PROPN
ejpam-5846	84	40	with	with	ADP
ejpam-5846	84	41	the	the	DET
ejpam-5846	84	42	given	give	VERB
ejpam-5846	84	43	angles	angle	NOUN
ejpam-5846	84	44	)	)	PUNCT
ejpam-5846	84	45	outside	outside	ADP
ejpam-5846	84	46	the	the	DET
ejpam-5846	84	47	given	give	VERB
ejpam-5846	84	48	triangle	triangle	NOUN
ejpam-5846	84	49	on	on	ADP
ejpam-5846	84	50	the	the	DET
ejpam-5846	84	51	segment	segment	NOUN
ejpam-5846	84	52	bc	bc	PROPN
ejpam-5846	84	53	we	we	PRON
ejpam-5846	84	54	construct	construct	VERB
ejpam-5846	84	55	an	an	DET
ejpam-5846	84	56	equilateral	equilateral	ADJ
ejpam-5846	84	57	triangle	triangle	NOUN
ejpam-5846	84	58	bce	bce	PROPN
ejpam-5846	84	59	.	.	PUNCT
ejpam-5846	85	1	then	then	ADV
ejpam-5846	85	2	,	,	PUNCT
ejpam-5846	85	3	as	as	SCONJ
ejpam-5846	85	4	ab	ab	PROPN
ejpam-5846	85	5	=	=	VERB
ejpam-5846	85	6	be	be	AUX
ejpam-5846	85	7	,	,	PUNCT
ejpam-5846	85	8	we	we	PRON
ejpam-5846	85	9	have	have	VERB
ejpam-5846	85	10	∠bae	∠bae	PROPN
ejpam-5846	85	11	=	=	SYM
ejpam-5846	85	12	∠bea	∠bea	PROPN
ejpam-5846	85	13	=	=	SYM
ejpam-5846	85	14	10	10	NUM
ejpam-5846	85	15	◦	◦	NOUN
ejpam-5846	85	16	.	.	PUNCT
ejpam-5846	86	1	and	and	CCONJ
ejpam-5846	86	2	the	the	DET
ejpam-5846	86	3	triangle	triangle	NOUN
ejpam-5846	86	4	abe	abe	PROPN
ejpam-5846	86	5	is	be	AUX
ejpam-5846	86	6	isosceles	isoscele	NOUN
ejpam-5846	86	7	.	.	PUNCT
ejpam-5846	87	1	in	in	ADP
ejpam-5846	87	2	the	the	DET
ejpam-5846	87	3	triangle	triangle	NOUN
ejpam-5846	87	4	ace	ace	NOUN
ejpam-5846	87	5	we	we	PRON
ejpam-5846	87	6	find	find	VERB
ejpam-5846	87	7	∠ace	∠ace	PROPN
ejpam-5846	87	8	=	=	PUNCT
ejpam-5846	87	9	100	100	NUM
ejpam-5846	87	10	◦	◦	NOUN
ejpam-5846	87	11	,∠eac	,∠eac	PUNCT
ejpam-5846	87	12	=	=	SYM
ejpam-5846	87	13	30	30	NUM
ejpam-5846	87	14	◦	◦	NOUN
ejpam-5846	87	15	and	and	CCONJ
ejpam-5846	87	16	∠aec	∠aec	NOUN
ejpam-5846	87	17	=	=	SYM
ejpam-5846	87	18	50	50	NUM
ejpam-5846	87	19	◦	◦	NOUN
ejpam-5846	87	20	.	.	PUNCT
ejpam-5846	88	1	since	since	SCONJ
ejpam-5846	88	2	ec	ec	PROPN
ejpam-5846	88	3	=	=	SYM
ejpam-5846	88	4	ab	ab	PROPN
ejpam-5846	88	5	,	,	PUNCT
ejpam-5846	88	6	ac	ac	PROPN
ejpam-5846	88	7	=	=	PUNCT
ejpam-5846	88	8	bd	bd	PROPN
ejpam-5846	88	9	and	and	CCONJ
ejpam-5846	88	10	∠ace	∠ace	PROPN
ejpam-5846	88	11	=	=	SYM
ejpam-5846	88	12	∠abd	∠abd	NOUN
ejpam-5846	88	13	=	=	PROPN
ejpam-5846	88	14	100	100	NUM
ejpam-5846	88	15	◦	◦	NOUN
ejpam-5846	88	16	,	,	PUNCT
ejpam-5846	88	17	then	then	ADV
ejpam-5846	88	18	the	the	DET
ejpam-5846	88	19	triangles	triangle	NOUN
ejpam-5846	88	20	eac	eac	PROPN
ejpam-5846	88	21	and	and	CCONJ
ejpam-5846	88	22	adb	adb	NOUN
ejpam-5846	88	23	are	be	AUX
ejpam-5846	88	24	equal	equal	ADJ
ejpam-5846	88	25	.	.	PUNCT
ejpam-5846	89	1	consequently	consequently	ADV
ejpam-5846	89	2	,	,	PUNCT
ejpam-5846	89	3	∠bad	∠bad	PROPN
ejpam-5846	89	4	=	=	PROPN
ejpam-5846	89	5	50	50	NUM
ejpam-5846	89	6	◦	◦	NOUN
ejpam-5846	89	7	,	,	PUNCT
ejpam-5846	89	8	and	and	CCONJ
ejpam-5846	89	9	therefore	therefore	ADV
ejpam-5846	89	10	,	,	PUNCT
ejpam-5846	89	11	∠cad	∠cad	PROPN
ejpam-5846	89	12	=	=	SYM
ejpam-5846	89	13	10	10	NUM
ejpam-5846	89	14	◦	◦	NOUN
ejpam-5846	89	15	.	.	PUNCT
ejpam-5846	90	1	(	(	PUNCT
ejpam-5846	90	2	fig.4	fig.4	PROPN
ejpam-5846	90	3	.	.	PUNCT
ejpam-5846	90	4	)	)	PUNCT
ejpam-5846	91	1	now	now	ADV
ejpam-5846	91	2	,	,	PUNCT
ejpam-5846	91	3	we	we	PRON
ejpam-5846	91	4	implement	implement	VERB
ejpam-5846	91	5	situation	situation	NOUN
ejpam-5846	91	6	3	3	NUM
ejpam-5846	91	7	in	in	ADP
ejpam-5846	91	8	solving	solve	VERB
ejpam-5846	91	9	the	the	DET
ejpam-5846	91	10	following	follow	VERB
ejpam-5846	91	11	problem	problem	NOUN
ejpam-5846	91	12	.	.	PUNCT
ejpam-5846	92	1	problem	problem	NOUN
ejpam-5846	92	2	3	3	X
ejpam-5846	92	3	.	.	PUNCT
ejpam-5846	93	1	let	let	VERB
ejpam-5846	93	2	m	m	PRON
ejpam-5846	93	3	be	be	AUX
ejpam-5846	93	4	the	the	DET
ejpam-5846	93	5	interior	interior	ADJ
ejpam-5846	93	6	point	point	NOUN
ejpam-5846	93	7	of	of	ADP
ejpam-5846	93	8	the	the	DET
ejpam-5846	93	9	triangle	triangle	NOUN
ejpam-5846	93	10	abc	abc	PROPN
ejpam-5846	93	11	,	,	PUNCT
ejpam-5846	93	12	∠mbc	∠mbc	PROPN
ejpam-5846	93	13	=	=	PUNCT
ejpam-5846	93	14	∠mcb	∠mcb	PUNCT
ejpam-5846	93	15	=	=	SYM
ejpam-5846	93	16	20	20	NUM
ejpam-5846	93	17	◦	◦	NOUN
ejpam-5846	93	18	and	and	CCONJ
ejpam-5846	93	19	ac	ac	NOUN
ejpam-5846	93	20	=	=	NOUN
ejpam-5846	93	21	cm	cm	NOUN
ejpam-5846	93	22	.	.	PUNCT
ejpam-5846	94	1	find	find	VERB
ejpam-5846	94	2	∠bam	∠bam	NOUN
ejpam-5846	94	3	.(fig.5	.(fig.5	NOUN
ejpam-5846	94	4	.	.	PUNCT
ejpam-5846	94	5	)	)	PUNCT
ejpam-5846	95	1	as	as	ADP
ejpam-5846	95	2	ac	ac	PROPN
ejpam-5846	95	3	=	=	PROPN
ejpam-5846	95	4	cm	cm	PROPN
ejpam-5846	95	5	,	,	PUNCT
ejpam-5846	95	6	the	the	DET
ejpam-5846	95	7	triangle	triangle	NOUN
ejpam-5846	95	8	amc	amc	PROPN
ejpam-5846	95	9	is	be	AUX
ejpam-5846	95	10	isosceles	isoscele	NOUN
ejpam-5846	95	11	and	and	CCONJ
ejpam-5846	95	12	∠mac	∠mac	PROPN
ejpam-5846	95	13	=	=	SYM
ejpam-5846	95	14	∠cma	∠cma	PROPN
ejpam-5846	95	15	=	=	PROPN
ejpam-5846	95	16	80	80	NUM
ejpam-5846	95	17	◦	◦	NOUN
ejpam-5846	95	18	.	.	PUNCT
ejpam-5846	96	1	on	on	ADP
ejpam-5846	96	2	the	the	DET
ejpam-5846	96	3	side	side	NOUN
ejpam-5846	96	4	bc	bc	PROPN
ejpam-5846	96	5	we	we	PRON
ejpam-5846	96	6	construct	construct	VERB
ejpam-5846	96	7	an	an	DET
ejpam-5846	96	8	equilateral	equilateral	ADJ
ejpam-5846	96	9	triangle	triangle	NOUN
ejpam-5846	96	10	dbc	dbc	PROPN
ejpam-5846	96	11	.	.	PUNCT
ejpam-5846	97	1	if	if	SCONJ
ejpam-5846	97	2	we	we	PRON
ejpam-5846	97	3	join	join	VERB
ejpam-5846	97	4	the	the	DET
ejpam-5846	97	5	points	point	NOUN
ejpam-5846	97	6	a	a	PRON
ejpam-5846	97	7	and	and	CCONJ
ejpam-5846	97	8	d	d	NOUN
ejpam-5846	97	9	,	,	PUNCT
ejpam-5846	97	10	then	then	ADV
ejpam-5846	97	11	the	the	DET
ejpam-5846	97	12	triangle	triangle	NOUN
ejpam-5846	97	13	cad	cad	PROPN
ejpam-5846	97	14	will	will	AUX
ejpam-5846	97	15	be	be	AUX
ejpam-5846	97	16	equal	equal	ADJ
ejpam-5846	97	17	to	to	ADP
ejpam-5846	97	18	the	the	DET
ejpam-5846	97	19	triangle	triangle	NOUN
ejpam-5846	97	20	cmb	cmb	NOUN
ejpam-5846	97	21	,	,	PUNCT
ejpam-5846	97	22	because	because	SCONJ
ejpam-5846	97	23	bc	bc	PROPN
ejpam-5846	97	24	=	=	PROPN
ejpam-5846	97	25	cd	cd	PROPN
ejpam-5846	97	26	,	,	PUNCT
ejpam-5846	97	27	ac	ac	PROPN
ejpam-5846	97	28	=	=	PROPN
ejpam-5846	97	29	cm	cm	PROPN
ejpam-5846	97	30	and	and	CCONJ
ejpam-5846	97	31	∠mcb	∠mcb	NOUN
ejpam-5846	97	32	=	=	SYM
ejpam-5846	97	33	∠acd	∠acd	NOUN
ejpam-5846	97	34	=	=	SYM
ejpam-5846	97	35	20	20	NUM
ejpam-5846	97	36	◦	◦	NOUN
ejpam-5846	97	37	.	.	PUNCT
ejpam-5846	98	1	from	from	ADP
ejpam-5846	98	2	here	here	ADV
ejpam-5846	98	3	,	,	PUNCT
ejpam-5846	98	4	we	we	PRON
ejpam-5846	98	5	have	have	VERB
ejpam-5846	98	6	∠adc	∠adc	NOUN
ejpam-5846	98	7	=	=	SYM
ejpam-5846	98	8	20	20	NUM
ejpam-5846	98	9	◦	◦	NOUN
ejpam-5846	98	10	and	and	CCONJ
ejpam-5846	98	11	ac	ac	ADJ
ejpam-5846	98	12	=	=	NOUN
ejpam-5846	98	13	ad	ad	NOUN
ejpam-5846	98	14	.	.	PUNCT
ejpam-5846	99	1	(	(	PUNCT
ejpam-5846	99	2	fig.6	fig.6	PROPN
ejpam-5846	99	3	.	.	PUNCT
ejpam-5846	99	4	)	)	PUNCT
ejpam-5846	100	1	on	on	ADP
ejpam-5846	100	2	the	the	DET
ejpam-5846	100	3	other	other	ADJ
ejpam-5846	100	4	hand	hand	NOUN
ejpam-5846	100	5	,	,	PUNCT
ejpam-5846	100	6	as	as	SCONJ
ejpam-5846	100	7	bd	bd	PROPN
ejpam-5846	100	8	=	=	PUNCT
ejpam-5846	100	9	bc	bc	PROPN
ejpam-5846	100	10	and	and	CCONJ
ejpam-5846	100	11	ac	ac	PROPN
ejpam-5846	100	12	=	=	PROPN
ejpam-5846	100	13	ad	ad	NOUN
ejpam-5846	100	14	,	,	PUNCT
ejpam-5846	100	15	then	then	ADV
ejpam-5846	100	16	the	the	DET
ejpam-5846	100	17	triangles	triangle	NOUN
ejpam-5846	100	18	bda	bda	PROPN
ejpam-5846	100	19	and	and	CCONJ
ejpam-5846	100	20	bca	bca	PROPN
ejpam-5846	100	21	s.	s.	PROPN
ejpam-5846	100	22	j.	j.	PROPN
ejpam-5846	100	23	aliyev	aliyev	PROPN
ejpam-5846	100	24	,	,	PUNCT
ejpam-5846	100	25	m.	m.	PROPN
ejpam-5846	100	26	n.	n.	PROPN
ejpam-5846	100	27	heydarova	heydarova	PROPN
ejpam-5846	100	28	,	,	PUNCT
ejpam-5846	100	29	a.	a.	NOUN
ejpam-5846	100	30	m.	m.	PROPN
ejpam-5846	100	31	seyidova	seyidova	PROPN
ejpam-5846	100	32	/	/	SYM
ejpam-5846	100	33	eur	eur	PROPN
ejpam-5846	100	34	.	.	PUNCT
ejpam-5846	101	1	j.	j.	PROPN
ejpam-5846	101	2	pure	pure	PROPN
ejpam-5846	101	3	appl	appl	PROPN
ejpam-5846	101	4	.	.	PROPN
ejpam-5846	101	5	math	math	PROPN
ejpam-5846	101	6	,	,	PUNCT
ejpam-5846	101	7	18	18	NUM
ejpam-5846	101	8	(	(	PUNCT
ejpam-5846	101	9	1	1	NUM
ejpam-5846	101	10	)	)	PUNCT
ejpam-5846	101	11	(	(	PUNCT
ejpam-5846	101	12	2025	2025	NUM
ejpam-5846	101	13	)	)	PUNCT
ejpam-5846	101	14	,	,	PUNCT
ejpam-5846	101	15	5846	5846	NUM
ejpam-5846	101	16	7	7	NUM
ejpam-5846	101	17	of	of	ADP
ejpam-5846	101	18	9	9	NUM
ejpam-5846	101	19	figure	figure	NOUN
ejpam-5846	101	20	8	8	NUM
ejpam-5846	101	21	:	:	PUNCT
ejpam-5846	101	22	(	(	PUNCT
ejpam-5846	101	23	triangle	triangle	NOUN
ejpam-5846	101	24	cmd	cmd	NOUN
ejpam-5846	101	25	is	be	AUX
ejpam-5846	101	26	equilateral	equilateral	ADJ
ejpam-5846	101	27	,	,	PUNCT
ejpam-5846	101	28	while	while	SCONJ
ejpam-5846	101	29	triangles	triangle	NOUN
ejpam-5846	101	30	cad	cad	PROPN
ejpam-5846	101	31	and	and	CCONJ
ejpam-5846	101	32	cma	cma	PROPN
ejpam-5846	101	33	are	be	AUX
ejpam-5846	101	34	isosceles	isoscele	NOUN
ejpam-5846	101	35	)	)	PUNCT
ejpam-5846	101	36	are	be	AUX
ejpam-5846	101	37	equal	equal	ADJ
ejpam-5846	101	38	.	.	PUNCT
ejpam-5846	102	1	consequently	consequently	ADV
ejpam-5846	102	2	,	,	PUNCT
ejpam-5846	102	3	∠dba	∠dba	PROPN
ejpam-5846	102	4	=	=	SYM
ejpam-5846	102	5	∠cba	∠cba	PROPN
ejpam-5846	102	6	=	=	SYM
ejpam-5846	102	7	30	30	NUM
ejpam-5846	102	8	◦	◦	NOUN
ejpam-5846	102	9	,	,	PUNCT
ejpam-5846	102	10	and	and	CCONJ
ejpam-5846	102	11	therefore,∠abm	therefore,∠abm	X
ejpam-5846	102	12	=	=	SYM
ejpam-5846	102	13	10	10	NUM
ejpam-5846	102	14	◦	◦	NOUN
ejpam-5846	102	15	.	.	PUNCT
ejpam-5846	102	16	from	from	ADP
ejpam-5846	102	17	the	the	DET
ejpam-5846	102	18	triangle	triangle	NOUN
ejpam-5846	102	19	abc	abc	PROPN
ejpam-5846	102	20	we	we	PRON
ejpam-5846	102	21	have	have	VERB
ejpam-5846	102	22	∠bam	∠bam	NOUN
ejpam-5846	102	23	=	=	SYM
ejpam-5846	102	24	30	30	NUM
ejpam-5846	102	25	◦	◦	NOUN
ejpam-5846	102	26	.	.	PUNCT
ejpam-5846	103	1	finally	finally	ADV
ejpam-5846	103	2	,	,	PUNCT
ejpam-5846	103	3	we	we	PRON
ejpam-5846	103	4	implement	implement	VERB
ejpam-5846	103	5	situation	situation	NOUN
ejpam-5846	103	6	4	4	NUM
ejpam-5846	103	7	with	with	ADP
ejpam-5846	103	8	our	our	PRON
ejpam-5846	103	9	new	new	ADJ
ejpam-5846	103	10	method	method	NOUN
ejpam-5846	103	11	on	on	ADP
ejpam-5846	103	12	the	the	DET
ejpam-5846	103	13	problem	problem	NOUN
ejpam-5846	103	14	solved	solve	VERB
ejpam-5846	103	15	by	by	ADP
ejpam-5846	103	16	using	use	VERB
ejpam-5846	103	17	the	the	DET
ejpam-5846	103	18	method	method	NOUN
ejpam-5846	103	19	of	of	ADP
ejpam-5846	103	20	auxiliary	auxiliary	ADJ
ejpam-5846	103	21	circle	circle	NOUN
ejpam-5846	103	22	divided	divide	VERB
ejpam-5846	103	23	into	into	ADP
ejpam-5846	103	24	equal	equal	ADJ
ejpam-5846	103	25	parts	part	NOUN
ejpam-5846	103	26	[	[	X
ejpam-5846	103	27	1	1	NUM
ejpam-5846	103	28	]	]	PUNCT
ejpam-5846	103	29	.	.	PUNCT
ejpam-5846	104	1	problem	problem	NOUN
ejpam-5846	104	2	4	4	NUM
ejpam-5846	104	3	.	.	PUNCT
ejpam-5846	105	1	the	the	DET
ejpam-5846	105	2	point	point	NOUN
ejpam-5846	105	3	m	m	AUX
ejpam-5846	105	4	is	be	AUX
ejpam-5846	105	5	given	give	VERB
ejpam-5846	105	6	inside	inside	ADP
ejpam-5846	105	7	the	the	DET
ejpam-5846	105	8	triangle	triangle	NOUN
ejpam-5846	105	9	abc	abc	PROPN
ejpam-5846	105	10	so	so	SCONJ
ejpam-5846	105	11	that	that	SCONJ
ejpam-5846	105	12	∠abm	∠abm	PROPN
ejpam-5846	105	13	=	=	SYM
ejpam-5846	105	14	∠cbm	∠cbm	VERB
ejpam-5846	105	15	=	=	SYM
ejpam-5846	105	16	∠bcm	∠bcm	PROPN
ejpam-5846	105	17	=	=	SYM
ejpam-5846	105	18	15	15	NUM
ejpam-5846	105	19	◦	◦	NOUN
ejpam-5846	105	20	and	and	CCONJ
ejpam-5846	105	21	∠acm	∠acm	PROPN
ejpam-5846	105	22	=	=	NOUN
ejpam-5846	105	23	30	30	NUM
ejpam-5846	105	24	◦	◦	NOUN
ejpam-5846	105	25	.	.	PUNCT
ejpam-5846	105	26	prove	prove	VERB
ejpam-5846	105	27	that	that	SCONJ
ejpam-5846	105	28	∠cam	∠cam	PROPN
ejpam-5846	105	29	=	=	SYM
ejpam-5846	105	30	75	75	NUM
ejpam-5846	105	31	◦	◦	NOUN
ejpam-5846	105	32	.	.	PUNCT
ejpam-5846	106	1	let	let	VERB
ejpam-5846	106	2	the	the	DET
ejpam-5846	106	3	circle	circle	NOUN
ejpam-5846	106	4	centered	center	VERB
ejpam-5846	106	5	at	at	ADP
ejpam-5846	106	6	m	m	PROPN
ejpam-5846	106	7	with	with	ADP
ejpam-5846	106	8	a	a	DET
ejpam-5846	106	9	radius	radius	NOUN
ejpam-5846	106	10	bm	bm	NOUN
ejpam-5846	106	11	=	=	PROPN
ejpam-5846	106	12	mc	mc	PROPN
ejpam-5846	106	13	intersect	intersect	VERB
ejpam-5846	106	14	the	the	DET
ejpam-5846	106	15	continuation	continuation	NOUN
ejpam-5846	106	16	of	of	ADP
ejpam-5846	106	17	ab	ab	PROPN
ejpam-5846	106	18	at	at	ADP
ejpam-5846	106	19	the	the	DET
ejpam-5846	106	20	point	point	NOUN
ejpam-5846	106	21	d.	d.	PROPN
ejpam-5846	106	22	then	then	ADV
ejpam-5846	106	23	,	,	PUNCT
ejpam-5846	106	24	as	as	SCONJ
ejpam-5846	106	25	dm	dm	PROPN
ejpam-5846	106	26	=	=	PUNCT
ejpam-5846	106	27	bm	bm	PROPN
ejpam-5846	106	28	,	,	PUNCT
ejpam-5846	106	29	the	the	DET
ejpam-5846	106	30	triangle	triangle	NOUN
ejpam-5846	106	31	dbm	dbm	PROPN
ejpam-5846	106	32	is	be	AUX
ejpam-5846	106	33	isosceles	isoscele	NOUN
ejpam-5846	106	34	and	and	CCONJ
ejpam-5846	106	35	∠dbm	∠dbm	PROPN
ejpam-5846	106	36	=	=	SYM
ejpam-5846	106	37	∠bdm	∠bdm	PROPN
ejpam-5846	106	38	=	=	SYM
ejpam-5846	106	39	15	15	NUM
ejpam-5846	106	40	◦	◦	NOUN
ejpam-5846	106	41	.	.	PUNCT
ejpam-5846	107	1	(	(	PUNCT
ejpam-5846	107	2	fig.7	fig.7	ADJ
ejpam-5846	107	3	.	.	PUNCT
ejpam-5846	107	4	)	)	PUNCT
ejpam-5846	108	1	connecting	connect	VERB
ejpam-5846	108	2	points	point	NOUN
ejpam-5846	108	3	d	d	NOUN
ejpam-5846	108	4	and	and	CCONJ
ejpam-5846	108	5	c	c	PROPN
ejpam-5846	108	6	,	,	PUNCT
ejpam-5846	108	7	taking	take	VERB
ejpam-5846	108	8	into	into	ADP
ejpam-5846	108	9	account	account	NOUN
ejpam-5846	109	1	∠dbm	∠dbm	PROPN
ejpam-5846	109	2	=	=	SYM
ejpam-5846	110	1	∠cmb	∠cmb	PROPN
ejpam-5846	110	2	=	=	NUM
ejpam-5846	110	3	150	150	NUM
ejpam-5846	110	4	◦	◦	NOUN
ejpam-5846	110	5	we	we	PRON
ejpam-5846	110	6	get	get	VERB
ejpam-5846	110	7	an	an	DET
ejpam-5846	110	8	equilateral	equilateral	ADJ
ejpam-5846	110	9	triangle	triangle	NOUN
ejpam-5846	110	10	dmc	dmc	NOUN
ejpam-5846	110	11	.	.	PUNCT
ejpam-5846	111	1	in	in	ADP
ejpam-5846	111	2	the	the	DET
ejpam-5846	111	3	triangle	triangle	NOUN
ejpam-5846	111	4	acd	acd	NOUN
ejpam-5846	111	5	,	,	PUNCT
ejpam-5846	111	6	we	we	PRON
ejpam-5846	111	7	find	find	VERB
ejpam-5846	111	8	∠cad	∠cad	PROPN
ejpam-5846	111	9	=	=	SYM
ejpam-5846	111	10	180	180	NUM
ejpam-5846	111	11	◦	◦	NOUN
ejpam-5846	111	12	−	−	X
ejpam-5846	111	13	(	(	PUNCT
ejpam-5846	111	14	30	30	NUM
ejpam-5846	111	15	◦	◦	NOUN
ejpam-5846	111	16	+	+	NUM
ejpam-5846	111	17	75	75	NUM
ejpam-5846	111	18	◦	◦	NOUN
ejpam-5846	111	19	)	)	PUNCT
ejpam-5846	111	20	=	=	SYM
ejpam-5846	111	21	75	75	NUM
ejpam-5846	111	22	◦	◦	NOUN
ejpam-5846	111	23	.	.	PUNCT
ejpam-5846	112	1	hence	hence	ADV
ejpam-5846	112	2	,	,	PUNCT
ejpam-5846	112	3	ca	ca	NOUN
ejpam-5846	112	4	=	=	SYM
ejpam-5846	112	5	cd	cd	PROPN
ejpam-5846	112	6	.	.	PUNCT
ejpam-5846	113	1	on	on	ADP
ejpam-5846	113	2	the	the	DET
ejpam-5846	113	3	other	other	ADJ
ejpam-5846	113	4	hand	hand	NOUN
ejpam-5846	113	5	,	,	PUNCT
ejpam-5846	113	6	as	as	ADP
ejpam-5846	113	7	cd	cd	PROPN
ejpam-5846	113	8	=	=	PUNCT
ejpam-5846	113	9	cm	cm	NOUN
ejpam-5846	113	10	,	,	PUNCT
ejpam-5846	113	11	we	we	PRON
ejpam-5846	113	12	have	have	VERB
ejpam-5846	113	13	ca	ca	NOUN
ejpam-5846	113	14	=	=	SYM
ejpam-5846	113	15	cm	cm	NOUN
ejpam-5846	113	16	,	,	PUNCT
ejpam-5846	113	17	i.e.	i.e.	X
ejpam-5846	113	18	the	the	DET
ejpam-5846	113	19	triangle	triangle	NOUN
ejpam-5846	113	20	cam	cam	NOUN
ejpam-5846	113	21	is	be	AUX
ejpam-5846	113	22	isosceles	isoscele	NOUN
ejpam-5846	113	23	.	.	PUNCT
ejpam-5846	114	1	consequently	consequently	ADV
ejpam-5846	114	2	,	,	PUNCT
ejpam-5846	114	3	∠cam	∠cam	PROPN
ejpam-5846	114	4	=	=	PUNCT
ejpam-5846	114	5	75	75	NUM
ejpam-5846	114	6	◦	◦	NOUN
ejpam-5846	114	7	.	.	PUNCT
ejpam-5846	115	1	(	(	PUNCT
ejpam-5846	115	2	fig.8	fig.8	PROPN
ejpam-5846	115	3	.	.	PUNCT
ejpam-5846	115	4	)	)	PUNCT
ejpam-5846	116	1	this	this	DET
ejpam-5846	116	2	example	example	NOUN
ejpam-5846	116	3	shows	show	VERB
ejpam-5846	116	4	that	that	SCONJ
ejpam-5846	116	5	many	many	ADJ
ejpam-5846	116	6	problems	problem	NOUN
ejpam-5846	116	7	,	,	PUNCT
ejpam-5846	116	8	even	even	ADV
ejpam-5846	116	9	very	very	ADV
ejpam-5846	116	10	difficult	difficult	ADJ
ejpam-5846	116	11	ones	one	NOUN
ejpam-5846	116	12	,	,	PUNCT
ejpam-5846	116	13	can	can	AUX
ejpam-5846	116	14	ben	ben	PROPN
ejpam-5846	116	15	solved	solve	VERB
ejpam-5846	116	16	using	use	VERB
ejpam-5846	116	17	method	method	NOUN
ejpam-5846	116	18	of	of	ADP
ejpam-5846	116	19	introducing	introduce	VERB
ejpam-5846	116	20	an	an	DET
ejpam-5846	116	21	equilateral	equilateral	ADJ
ejpam-5846	116	22	triangle	triangle	NOUN
ejpam-5846	116	23	.	.	PUNCT
ejpam-5846	117	1	3	3	X
ejpam-5846	117	2	.	.	X
ejpam-5846	117	3	concluding	conclude	VERB
ejpam-5846	117	4	remarks	remark	NOUN
ejpam-5846	117	5	this	this	DET
ejpam-5846	117	6	study	study	NOUN
ejpam-5846	117	7	provides	provide	VERB
ejpam-5846	117	8	an	an	DET
ejpam-5846	117	9	in	in	ADP
ejpam-5846	117	10	-	-	PUNCT
ejpam-5846	117	11	depth	depth	NOUN
ejpam-5846	117	12	examination	examination	NOUN
ejpam-5846	117	13	of	of	ADP
ejpam-5846	117	14	using	use	VERB
ejpam-5846	117	15	the	the	DET
ejpam-5846	117	16	equilateral	equilateral	ADJ
ejpam-5846	117	17	triangle	triangle	NOUN
ejpam-5846	117	18	as	as	ADP
ejpam-5846	117	19	an	an	DET
ejpam-5846	117	20	auxiliary	auxiliary	ADJ
ejpam-5846	117	21	element	element	NOUN
ejpam-5846	117	22	in	in	ADP
ejpam-5846	117	23	solving	solve	VERB
ejpam-5846	117	24	geometric	geometric	ADJ
ejpam-5846	117	25	(	(	PUNCT
ejpam-5846	117	26	planimetric	planimetric	ADJ
ejpam-5846	117	27	)	)	PUNCT
ejpam-5846	117	28	problems	problem	NOUN
ejpam-5846	117	29	.	.	PUNCT
ejpam-5846	118	1	especially	especially	ADV
ejpam-5846	118	2	in	in	ADP
ejpam-5846	118	3	planimetric	planimetric	ADJ
ejpam-5846	118	4	problems	problem	NOUN
ejpam-5846	118	5	,	,	PUNCT
ejpam-5846	118	6	the	the	DET
ejpam-5846	118	7	use	use	NOUN
ejpam-5846	118	8	of	of	ADP
ejpam-5846	118	9	an	an	DET
ejpam-5846	118	10	equilateral	equilateral	ADJ
ejpam-5846	118	11	triangle	triangle	NOUN
ejpam-5846	118	12	shows	show	VERB
ejpam-5846	118	13	potential	potential	NOUN
ejpam-5846	118	14	for	for	ADP
ejpam-5846	118	15	simplifying	simplify	VERB
ejpam-5846	118	16	the	the	DET
ejpam-5846	118	17	problemsolving	problemsolving	NOUN
ejpam-5846	118	18	process	process	NOUN
ejpam-5846	118	19	,	,	PUNCT
ejpam-5846	118	20	enhancing	enhance	VERB
ejpam-5846	118	21	intuition	intuition	NOUN
ejpam-5846	118	22	,	,	PUNCT
ejpam-5846	118	23	and	and	CCONJ
ejpam-5846	118	24	achieving	achieve	VERB
ejpam-5846	118	25	more	more	ADV
ejpam-5846	118	26	efficient	efficient	ADJ
ejpam-5846	118	27	solutions	solution	NOUN
ejpam-5846	118	28	.	.	PUNCT
ejpam-5846	119	1	four	four	NUM
ejpam-5846	119	2	distinct	distinct	ADJ
ejpam-5846	119	3	cases	case	NOUN
ejpam-5846	119	4	for	for	ADP
ejpam-5846	119	5	applying	apply	VERB
ejpam-5846	119	6	this	this	DET
ejpam-5846	119	7	method	method	NOUN
ejpam-5846	119	8	were	be	AUX
ejpam-5846	119	9	explored	explore	VERB
ejpam-5846	119	10	,	,	PUNCT
ejpam-5846	119	11	each	each	PRON
ejpam-5846	119	12	illustrated	illustrate	VERB
ejpam-5846	119	13	with	with	ADP
ejpam-5846	119	14	example	example	NOUN
ejpam-5846	119	15	problem	problem	NOUN
ejpam-5846	119	16	solutions	solution	NOUN
ejpam-5846	119	17	.	.	PUNCT
ejpam-5846	120	1	these	these	DET
ejpam-5846	120	2	examples	example	NOUN
ejpam-5846	120	3	demonstrate	demonstrate	VERB
ejpam-5846	120	4	that	that	SCONJ
ejpam-5846	120	5	the	the	DET
ejpam-5846	120	6	method	method	NOUN
ejpam-5846	120	7	is	be	AUX
ejpam-5846	120	8	applicable	applicable	ADJ
ejpam-5846	120	9	to	to	ADP
ejpam-5846	120	10	a	a	DET
ejpam-5846	120	11	wide	wide	ADJ
ejpam-5846	120	12	range	range	NOUN
ejpam-5846	120	13	of	of	ADP
ejpam-5846	120	14	problems	problem	NOUN
ejpam-5846	120	15	and	and	CCONJ
ejpam-5846	120	16	contributes	contribute	VERB
ejpam-5846	120	17	significantly	significantly	ADV
ejpam-5846	120	18	to	to	ADP
ejpam-5846	120	19	solution	solution	NOUN
ejpam-5846	120	20	processes	process	NOUN
ejpam-5846	120	21	.	.	PUNCT
ejpam-5846	121	1	s.	s.	PROPN
ejpam-5846	121	2	j.	j.	PROPN
ejpam-5846	121	3	aliyev	aliyev	PROPN
ejpam-5846	121	4	,	,	PUNCT
ejpam-5846	121	5	m.	m.	PROPN
ejpam-5846	121	6	n.	n.	PROPN
ejpam-5846	121	7	heydarova	heydarova	PROPN
ejpam-5846	121	8	,	,	PUNCT
ejpam-5846	121	9	a.	a.	NOUN
ejpam-5846	121	10	m.	m.	PROPN
ejpam-5846	121	11	seyidova	seyidova	PROPN
ejpam-5846	121	12	/	/	SYM
ejpam-5846	121	13	eur	eur	PROPN
ejpam-5846	121	14	.	.	PUNCT
ejpam-5846	122	1	j.	j.	PROPN
ejpam-5846	122	2	pure	pure	PROPN
ejpam-5846	122	3	appl	appl	PROPN
ejpam-5846	122	4	.	.	PROPN
ejpam-5846	122	5	math	math	PROPN
ejpam-5846	122	6	,	,	PUNCT
ejpam-5846	122	7	18	18	NUM
ejpam-5846	122	8	(	(	PUNCT
ejpam-5846	122	9	1	1	NUM
ejpam-5846	122	10	)	)	PUNCT
ejpam-5846	122	11	(	(	PUNCT
ejpam-5846	122	12	2025	2025	NUM
ejpam-5846	122	13	)	)	PUNCT
ejpam-5846	122	14	,	,	PUNCT
ejpam-5846	122	15	5846	5846	NUM
ejpam-5846	122	16	8	8	NUM
ejpam-5846	122	17	of	of	ADP
ejpam-5846	122	18	9	9	NUM
ejpam-5846	122	19	the	the	DET
ejpam-5846	122	20	method	method	NOUN
ejpam-5846	122	21	draws	draw	VERB
ejpam-5846	122	22	on	on	ADP
ejpam-5846	122	23	classical	classical	ADJ
ejpam-5846	122	24	geometry	geometry	NOUN
ejpam-5846	122	25	principles	principle	NOUN
ejpam-5846	122	26	and	and	CCONJ
ejpam-5846	122	27	concepts	concept	NOUN
ejpam-5846	122	28	of	of	ADP
ejpam-5846	122	29	symmetry	symmetry	NOUN
ejpam-5846	122	30	.	.	PUNCT
ejpam-5846	123	1	auxiliary	auxiliary	ADJ
ejpam-5846	123	2	elements	element	NOUN
ejpam-5846	123	3	like	like	ADP
ejpam-5846	123	4	the	the	DET
ejpam-5846	123	5	equilateral	equilateral	ADJ
ejpam-5846	123	6	triangle	triangle	NOUN
ejpam-5846	123	7	reveal	reveal	VERB
ejpam-5846	123	8	features	feature	NOUN
ejpam-5846	123	9	of	of	ADP
ejpam-5846	123	10	the	the	DET
ejpam-5846	123	11	problem	problem	NOUN
ejpam-5846	123	12	that	that	PRON
ejpam-5846	123	13	may	may	AUX
ejpam-5846	123	14	otherwise	otherwise	ADV
ejpam-5846	123	15	remain	remain	VERB
ejpam-5846	123	16	unnoticed	unnoticed	ADJ
ejpam-5846	123	17	,	,	PUNCT
ejpam-5846	123	18	guiding	guide	VERB
ejpam-5846	123	19	problem	problem	NOUN
ejpam-5846	123	20	-	-	PUNCT
ejpam-5846	123	21	solvers	solver	NOUN
ejpam-5846	123	22	towards	towards	ADP
ejpam-5846	123	23	solutions	solution	NOUN
ejpam-5846	123	24	.	.	PUNCT
ejpam-5846	124	1	in	in	ADP
ejpam-5846	124	2	this	this	DET
ejpam-5846	124	3	context	context	NOUN
ejpam-5846	124	4	,	,	PUNCT
ejpam-5846	124	5	the	the	DET
ejpam-5846	124	6	method	method	NOUN
ejpam-5846	124	7	contributes	contribute	VERB
ejpam-5846	124	8	to	to	ADP
ejpam-5846	124	9	developing	develop	VERB
ejpam-5846	124	10	intuitive	intuitive	ADJ
ejpam-5846	124	11	thinking	thinking	NOUN
ejpam-5846	124	12	skills	skill	NOUN
ejpam-5846	124	13	in	in	ADP
ejpam-5846	124	14	students	student	NOUN
ejpam-5846	124	15	and	and	CCONJ
ejpam-5846	124	16	problem	problem	NOUN
ejpam-5846	124	17	-	-	PUNCT
ejpam-5846	124	18	solvers	solver	NOUN
ejpam-5846	124	19	.	.	PUNCT
ejpam-5846	125	1	additionally	additionally	ADV
ejpam-5846	125	2	,	,	PUNCT
ejpam-5846	125	3	it	it	PRON
ejpam-5846	125	4	allows	allow	VERB
ejpam-5846	125	5	problems	problem	NOUN
ejpam-5846	125	6	to	to	PART
ejpam-5846	125	7	be	be	AUX
ejpam-5846	125	8	simplified	simplify	VERB
ejpam-5846	125	9	to	to	ADP
ejpam-5846	125	10	more	more	ADV
ejpam-5846	125	11	fundamental	fundamental	ADJ
ejpam-5846	125	12	forms	form	NOUN
ejpam-5846	125	13	,	,	PUNCT
ejpam-5846	125	14	enabling	enable	VERB
ejpam-5846	125	15	the	the	DET
ejpam-5846	125	16	effective	effective	ADJ
ejpam-5846	125	17	application	application	NOUN
ejpam-5846	125	18	of	of	ADP
ejpam-5846	125	19	existing	exist	VERB
ejpam-5846	125	20	geometric	geometric	ADJ
ejpam-5846	125	21	knowledge	knowledge	NOUN
ejpam-5846	125	22	.	.	PUNCT
ejpam-5846	126	1	research	research	NOUN
ejpam-5846	126	2	in	in	ADP
ejpam-5846	126	3	the	the	DET
ejpam-5846	126	4	literature	literature	NOUN
ejpam-5846	126	5	and	and	CCONJ
ejpam-5846	126	6	findings	finding	NOUN
ejpam-5846	126	7	from	from	ADP
ejpam-5846	126	8	this	this	DET
ejpam-5846	126	9	study	study	NOUN
ejpam-5846	126	10	indicate	indicate	VERB
ejpam-5846	126	11	that	that	SCONJ
ejpam-5846	126	12	using	use	VERB
ejpam-5846	126	13	auxiliary	auxiliary	ADJ
ejpam-5846	126	14	elements	element	NOUN
ejpam-5846	126	15	such	such	ADJ
ejpam-5846	126	16	as	as	ADP
ejpam-5846	126	17	the	the	DET
ejpam-5846	126	18	equilateral	equilateral	ADJ
ejpam-5846	126	19	triangle	triangle	NOUN
ejpam-5846	126	20	in	in	ADP
ejpam-5846	126	21	geometry	geometry	NOUN
ejpam-5846	126	22	education	education	NOUN
ejpam-5846	126	23	facilitates	facilitate	VERB
ejpam-5846	126	24	learning	learn	VERB
ejpam-5846	126	25	and	and	CCONJ
ejpam-5846	126	26	deepens	deepen	VERB
ejpam-5846	126	27	mathematical	mathematical	ADJ
ejpam-5846	126	28	understanding	understanding	NOUN
ejpam-5846	126	29	.	.	PUNCT
ejpam-5846	127	1	the	the	DET
ejpam-5846	127	2	method	method	NOUN
ejpam-5846	127	3	encourages	encourage	VERB
ejpam-5846	127	4	students	student	NOUN
ejpam-5846	127	5	to	to	PART
ejpam-5846	127	6	approach	approach	VERB
ejpam-5846	127	7	geometry	geometry	NOUN
ejpam-5846	127	8	problems	problem	NOUN
ejpam-5846	127	9	more	more	ADV
ejpam-5846	127	10	creatively	creatively	ADV
ejpam-5846	127	11	and	and	CCONJ
ejpam-5846	127	12	analytically	analytically	ADV
ejpam-5846	127	13	while	while	SCONJ
ejpam-5846	127	14	adding	add	VERB
ejpam-5846	127	15	an	an	DET
ejpam-5846	127	16	aesthetic	aesthetic	ADJ
ejpam-5846	127	17	dimension	dimension	NOUN
ejpam-5846	127	18	to	to	ADP
ejpam-5846	127	19	the	the	DET
ejpam-5846	127	20	solution	solution	NOUN
ejpam-5846	127	21	process	process	NOUN
ejpam-5846	127	22	.	.	PUNCT
ejpam-5846	128	1	in	in	ADP
ejpam-5846	128	2	the	the	DET
ejpam-5846	128	3	future	future	NOUN
ejpam-5846	128	4	,	,	PUNCT
ejpam-5846	128	5	it	it	PRON
ejpam-5846	128	6	will	will	AUX
ejpam-5846	128	7	be	be	AUX
ejpam-5846	128	8	important	important	ADJ
ejpam-5846	128	9	to	to	PART
ejpam-5846	128	10	examine	examine	VERB
ejpam-5846	128	11	the	the	DET
ejpam-5846	128	12	impact	impact	NOUN
ejpam-5846	128	13	of	of	ADP
ejpam-5846	128	14	this	this	DET
ejpam-5846	128	15	method	method	NOUN
ejpam-5846	128	16	on	on	ADP
ejpam-5846	128	17	a	a	DET
ejpam-5846	128	18	broader	broad	ADJ
ejpam-5846	128	19	range	range	NOUN
ejpam-5846	128	20	of	of	ADP
ejpam-5846	128	21	geometry	geometry	NOUN
ejpam-5846	128	22	problems	problem	NOUN
ejpam-5846	128	23	and	and	CCONJ
ejpam-5846	128	24	test	test	VERB
ejpam-5846	128	25	its	its	PRON
ejpam-5846	128	26	applicability	applicability	NOUN
ejpam-5846	128	27	across	across	ADP
ejpam-5846	128	28	various	various	ADJ
ejpam-5846	128	29	educational	educational	ADJ
ejpam-5846	128	30	levels	level	NOUN
ejpam-5846	128	31	.	.	PUNCT
ejpam-5846	129	1	for	for	ADP
ejpam-5846	129	2	example	example	NOUN
ejpam-5846	129	3	,	,	PUNCT
ejpam-5846	129	4	studies	study	NOUN
ejpam-5846	129	5	could	could	AUX
ejpam-5846	129	6	explore	explore	VERB
ejpam-5846	129	7	the	the	DET
ejpam-5846	129	8	method	method	NOUN
ejpam-5846	129	9	’s	’s	PART
ejpam-5846	129	10	effectiveness	effectiveness	NOUN
ejpam-5846	129	11	with	with	ADP
ejpam-5846	129	12	different	different	ADJ
ejpam-5846	129	13	age	age	NOUN
ejpam-5846	129	14	groups	group	NOUN
ejpam-5846	129	15	,	,	PUNCT
ejpam-5846	129	16	its	its	PRON
ejpam-5846	129	17	influence	influence	NOUN
ejpam-5846	129	18	on	on	ADP
ejpam-5846	129	19	students	student	NOUN
ejpam-5846	129	20	’	'	PUNCT
ejpam-5846	129	21	mathematical	mathematical	ADJ
ejpam-5846	129	22	thinking	thinking	NOUN
ejpam-5846	129	23	skills	skill	NOUN
ejpam-5846	129	24	,	,	PUNCT
ejpam-5846	129	25	or	or	CCONJ
ejpam-5846	129	26	its	its	PRON
ejpam-5846	129	27	potential	potential	NOUN
ejpam-5846	129	28	for	for	ADP
ejpam-5846	129	29	accelerating	accelerate	VERB
ejpam-5846	129	30	problem	problem	NOUN
ejpam-5846	129	31	-	-	PUNCT
ejpam-5846	129	32	solving	solve	VERB
ejpam-5846	129	33	processes	process	NOUN
ejpam-5846	129	34	.	.	PUNCT
ejpam-5846	130	1	such	such	ADJ
ejpam-5846	130	2	research	research	NOUN
ejpam-5846	130	3	could	could	AUX
ejpam-5846	130	4	help	help	VERB
ejpam-5846	130	5	integrate	integrate	VERB
ejpam-5846	130	6	this	this	DET
ejpam-5846	130	7	method	method	NOUN
ejpam-5846	130	8	into	into	ADP
ejpam-5846	130	9	educational	educational	ADJ
ejpam-5846	130	10	curricula	curricula	NOUN
ejpam-5846	130	11	on	on	ADP
ejpam-5846	130	12	a	a	DET
ejpam-5846	130	13	larger	large	ADJ
ejpam-5846	130	14	scale	scale	NOUN
ejpam-5846	130	15	,	,	PUNCT
ejpam-5846	130	16	making	make	VERB
ejpam-5846	130	17	geometry	geometry	NOUN
ejpam-5846	130	18	education	education	NOUN
ejpam-5846	130	19	more	more	ADV
ejpam-5846	130	20	effective	effective	ADJ
ejpam-5846	130	21	.	.	PUNCT
ejpam-5846	131	1	in	in	ADP
ejpam-5846	131	2	conclusion	conclusion	NOUN
ejpam-5846	131	3	,	,	PUNCT
ejpam-5846	131	4	using	use	VERB
ejpam-5846	131	5	the	the	DET
ejpam-5846	131	6	equilateral	equilateral	ADJ
ejpam-5846	131	7	triangle	triangle	NOUN
ejpam-5846	131	8	as	as	ADP
ejpam-5846	131	9	an	an	DET
ejpam-5846	131	10	auxiliary	auxiliary	ADJ
ejpam-5846	131	11	element	element	NOUN
ejpam-5846	131	12	in	in	ADP
ejpam-5846	131	13	planimetric	planimetric	ADJ
ejpam-5846	131	14	problems	problem	NOUN
ejpam-5846	131	15	emerges	emerge	VERB
ejpam-5846	131	16	as	as	ADP
ejpam-5846	131	17	a	a	DET
ejpam-5846	131	18	powerful	powerful	ADJ
ejpam-5846	131	19	tool	tool	NOUN
ejpam-5846	131	20	for	for	ADP
ejpam-5846	131	21	solving	solve	VERB
ejpam-5846	131	22	classical	classical	ADJ
ejpam-5846	131	23	geometry	geometry	NOUN
ejpam-5846	131	24	problems	problem	NOUN
ejpam-5846	131	25	.	.	PUNCT
ejpam-5846	132	1	by	by	ADP
ejpam-5846	132	2	simplifying	simplify	VERB
ejpam-5846	132	3	problem	problem	NOUN
ejpam-5846	132	4	-	-	PUNCT
ejpam-5846	132	5	solving	solve	VERB
ejpam-5846	132	6	processes	process	NOUN
ejpam-5846	132	7	and	and	CCONJ
ejpam-5846	132	8	offering	offer	VERB
ejpam-5846	132	9	an	an	DET
ejpam-5846	132	10	elegant	elegant	ADJ
ejpam-5846	132	11	solution	solution	NOUN
ejpam-5846	132	12	path	path	NOUN
ejpam-5846	132	13	,	,	PUNCT
ejpam-5846	132	14	this	this	DET
ejpam-5846	132	15	method	method	NOUN
ejpam-5846	132	16	holds	hold	VERB
ejpam-5846	132	17	valuable	valuable	ADJ
ejpam-5846	132	18	potential	potential	NOUN
ejpam-5846	132	19	for	for	ADP
ejpam-5846	132	20	developing	develop	VERB
ejpam-5846	132	21	innovative	innovative	ADJ
ejpam-5846	132	22	approaches	approach	NOUN
ejpam-5846	132	23	in	in	ADP
ejpam-5846	132	24	geometry	geometry	NOUN
ejpam-5846	132	25	teaching	teaching	NOUN
ejpam-5846	132	26	.	.	PUNCT
ejpam-5846	133	1	references	reference	NOUN
ejpam-5846	133	2	[	[	X
ejpam-5846	133	3	1	1	NUM
ejpam-5846	133	4	]	]	X
ejpam-5846	133	5	henry	henry	PROPN
ejpam-5846	133	6	africk	africk	PROPN
ejpam-5846	133	7	.	.	PUNCT
ejpam-5846	133	8	elementary	elementary	PROPN
ejpam-5846	133	9	college	college	PROPN
ejpam-5846	133	10	geometry	geometry	NOUN
ejpam-5846	133	11	.	.	PUNCT
ejpam-5846	134	1	cuny	cuny	PROPN
ejpam-5846	134	2	academic	academic	ADJ
ejpam-5846	134	3	works	work	NOUN
ejpam-5846	134	4	,	,	PUNCT
ejpam-5846	134	5	2021	2021	NUM
ejpam-5846	134	6	.	.	PUNCT
ejpam-5846	135	1	[	[	X
ejpam-5846	135	2	2	2	NUM
ejpam-5846	135	3	]	]	PUNCT
ejpam-5846	135	4	s.	s.	PROPN
ejpam-5846	135	5	aliyev	aliyev	PROPN
ejpam-5846	135	6	.	.	PUNCT
ejpam-5846	135	7	geometry	geometry	NOUN
ejpam-5846	135	8	.	.	PUNCT
ejpam-5846	136	1	tansel	tansel	PROPN
ejpam-5846	136	2	publications	publication	NOUN
ejpam-5846	136	3	,	,	PUNCT
ejpam-5846	136	4	adapazari	adapazari	NOUN
ejpam-5846	136	5	,	,	PUNCT
ejpam-5846	136	6	1996	1996	NUM
ejpam-5846	136	7	.	.	PUNCT
ejpam-5846	137	1	[	[	X
ejpam-5846	137	2	3	3	X
ejpam-5846	137	3	]	]	X
ejpam-5846	137	4	s.	s.	PROPN
ejpam-5846	137	5	aliyev	aliyev	PROPN
ejpam-5846	137	6	,	,	PUNCT
ejpam-5846	137	7	sh	sh	PROPN
ejpam-5846	137	8	.	.	PROPN
ejpam-5846	137	9	aghazade	aghazade	PROPN
ejpam-5846	137	10	,	,	PUNCT
ejpam-5846	137	11	and	and	CCONJ
ejpam-5846	137	12	g.	g.	PROPN
ejpam-5846	137	13	abdullayeva	abdullayeva	PROPN
ejpam-5846	137	14	.	.	PUNCT
ejpam-5846	138	1	using	use	VERB
ejpam-5846	138	2	area	area	NOUN
ejpam-5846	138	3	method	method	NOUN
ejpam-5846	138	4	in	in	ADP
ejpam-5846	138	5	secondary	secondary	ADJ
ejpam-5846	138	6	school	school	NOUN
ejpam-5846	138	7	geometry	geometry	NOUN
ejpam-5846	138	8	.	.	PUNCT
ejpam-5846	139	1	european	european	PROPN
ejpam-5846	139	2	journal	journal	PROPN
ejpam-5846	139	3	of	of	ADP
ejpam-5846	139	4	pure	pure	ADJ
ejpam-5846	139	5	and	and	CCONJ
ejpam-5846	139	6	applied	applied	ADJ
ejpam-5846	139	7	mathematics	mathematic	NOUN
ejpam-5846	139	8	,	,	PUNCT
ejpam-5846	139	9	14(2):601–607	14(2):601–607	PROPN
ejpam-5846	139	10	,	,	PUNCT
ejpam-5846	139	11	2021	2021	NUM
ejpam-5846	139	12	.	.	PUNCT
ejpam-5846	140	1	[	[	X
ejpam-5846	140	2	4	4	X
ejpam-5846	140	3	]	]	X
ejpam-5846	140	4	s.	s.	PROPN
ejpam-5846	140	5	aliyev	aliyev	PROPN
ejpam-5846	140	6	,	,	PUNCT
ejpam-5846	140	7	sh	sh	PROPN
ejpam-5846	140	8	.	.	PROPN
ejpam-5846	140	9	hamidova	hamidova	PROPN
ejpam-5846	140	10	,	,	PUNCT
ejpam-5846	140	11	and	and	CCONJ
ejpam-5846	140	12	g.	g.	PROPN
ejpam-5846	140	13	abdullayeva	abdullayeva	PROPN
ejpam-5846	140	14	.	.	PUNCT
ejpam-5846	141	1	some	some	DET
ejpam-5846	141	2	applications	application	NOUN
ejpam-5846	141	3	of	of	ADP
ejpam-5846	141	4	ptolemy	ptolemy	PROPN
ejpam-5846	141	5	’s	’s	PART
ejpam-5846	141	6	theorem	theorem	NOUN
ejpam-5846	141	7	in	in	ADP
ejpam-5846	141	8	secondary	secondary	ADJ
ejpam-5846	141	9	school	school	NOUN
ejpam-5846	141	10	mathematics	mathematic	NOUN
ejpam-5846	141	11	.	.	PUNCT
ejpam-5846	142	1	european	european	PROPN
ejpam-5846	142	2	journal	journal	PROPN
ejpam-5846	142	3	of	of	ADP
ejpam-5846	142	4	pure	pure	ADJ
ejpam-5846	142	5	and	and	CCONJ
ejpam-5846	142	6	applied	applied	ADJ
ejpam-5846	142	7	mathematics	mathematic	NOUN
ejpam-5846	142	8	,	,	PUNCT
ejpam-5846	142	9	13(1):180–184	13(1):180–184	PROPN
ejpam-5846	142	10	,	,	PUNCT
ejpam-5846	142	11	2020	2020	NUM
ejpam-5846	142	12	.	.	PUNCT
ejpam-5846	143	1	[	[	X
ejpam-5846	143	2	5	5	X
ejpam-5846	143	3	]	]	PUNCT
ejpam-5846	143	4	s.	s.	PROPN
ejpam-5846	143	5	aliyev	aliyev	PROPN
ejpam-5846	143	6	,	,	PUNCT
ejpam-5846	143	7	m.	m.	NOUN
ejpam-5846	143	8	heydarova	heydarova	PROPN
ejpam-5846	143	9	,	,	PUNCT
ejpam-5846	143	10	and	and	CCONJ
ejpam-5846	143	11	sh	sh	PROPN
ejpam-5846	143	12	.	.	PROPN
ejpam-5846	143	13	aghazade	aghazade	PROPN
ejpam-5846	143	14	.	.	PUNCT
ejpam-5846	144	1	solving	solve	VERB
ejpam-5846	144	2	geometry	geometry	NOUN
ejpam-5846	144	3	problems	problem	NOUN
ejpam-5846	144	4	by	by	ADP
ejpam-5846	144	5	alternative	alternative	ADJ
ejpam-5846	144	6	methods	method	NOUN
ejpam-5846	144	7	in	in	ADP
ejpam-5846	144	8	mathematics	mathematic	NOUN
ejpam-5846	144	9	education	education	NOUN
ejpam-5846	144	10	.	.	PUNCT
ejpam-5846	145	1	european	european	ADJ
ejpam-5846	145	2	journal	journal	PROPN
ejpam-5846	145	3	of	of	ADP
ejpam-5846	145	4	pure	pure	ADJ
ejpam-5846	145	5	and	and	CCONJ
ejpam-5846	145	6	applied	applied	ADJ
ejpam-5846	145	7	mathematics	mathematic	NOUN
ejpam-5846	145	8	,	,	PUNCT
ejpam-5846	145	9	16(2):1110–1117	16(2):1110–1117	NUM
ejpam-5846	145	10	,	,	PUNCT
ejpam-5846	145	11	2023	2023	NUM
ejpam-5846	145	12	.	.	PUNCT
ejpam-5846	146	1	[	[	X
ejpam-5846	146	2	6	6	NUM
ejpam-5846	146	3	]	]	PUNCT
ejpam-5846	146	4	a.	a.	NOUN
ejpam-5846	146	5	p.	p.	PROPN
ejpam-5846	146	6	kiselev	kiselev	PROPN
ejpam-5846	146	7	.	.	PUNCT
ejpam-5846	147	1	kiselev	kiselev	PROPN
ejpam-5846	147	2	’s	’s	PART
ejpam-5846	147	3	geometry	geometry	NOUN
ejpam-5846	147	4	,	,	PUNCT
ejpam-5846	147	5	book	book	NOUN
ejpam-5846	147	6	1	1	NUM
ejpam-5846	147	7	,	,	PUNCT
ejpam-5846	147	8	planimetry	planimetry	NOUN
ejpam-5846	147	9	.	.	PUNCT
ejpam-5846	148	1	sumizdat	sumizdat	PROPN
ejpam-5846	148	2	,	,	PUNCT
ejpam-5846	148	3	california	california	PROPN
ejpam-5846	148	4	,	,	PUNCT
ejpam-5846	148	5	2006	2006	NUM
ejpam-5846	148	6	.	.	PUNCT
ejpam-5846	149	1	[	[	X
ejpam-5846	149	2	7	7	NUM
ejpam-5846	149	3	]	]	PUNCT
ejpam-5846	149	4	ron	ron	PROPN
ejpam-5846	149	5	larson	larson	PROPN
ejpam-5846	149	6	,	,	PUNCT
ejpam-5846	149	7	laurie	laurie	PROPN
ejpam-5846	149	8	boswell	boswell	PROPN
ejpam-5846	149	9	,	,	PUNCT
ejpam-5846	149	10	and	and	CCONJ
ejpam-5846	149	11	lee	lee	PROPN
ejpam-5846	149	12	stiff	stiff	PROPN
ejpam-5846	149	13	.	.	PUNCT
ejpam-5846	149	14	geometry	geometry	NOUN
ejpam-5846	149	15	.	.	PUNCT
ejpam-5846	150	1	mcdougal	mcdougal	PROPN
ejpam-5846	150	2	littell	littell	PROPN
ejpam-5846	150	3	,	,	PUNCT
ejpam-5846	150	4	2004	2004	NUM
ejpam-5846	150	5	.	.	PUNCT
ejpam-5846	151	1	[	[	X
ejpam-5846	151	2	8	8	NUM
ejpam-5846	151	3	]	]	X
ejpam-5846	151	4	d.	d.	NOUN
ejpam-5846	151	5	pedoe	pedoe	PROPN
ejpam-5846	151	6	.	.	PUNCT
ejpam-5846	152	1	geometry	geometry	NOUN
ejpam-5846	152	2	:	:	PUNCT
ejpam-5846	152	3	a	a	DET
ejpam-5846	152	4	comprehensive	comprehensive	ADJ
ejpam-5846	152	5	course	course	NOUN
ejpam-5846	152	6	.	.	PUNCT
ejpam-5846	153	1	dover	dover	PROPN
ejpam-5846	153	2	publications	publication	NOUN
ejpam-5846	153	3	,	,	PUNCT
ejpam-5846	153	4	new	new	PROPN
ejpam-5846	153	5	york	york	PROPN
ejpam-5846	153	6	,	,	PUNCT
ejpam-5846	153	7	1988	1988	NUM
ejpam-5846	153	8	.	.	PUNCT
ejpam-5846	154	1	[	[	X
ejpam-5846	154	2	9	9	NUM
ejpam-5846	154	3	]	]	X
ejpam-5846	154	4	y.	y.	PROPN
ejpam-5846	154	5	p.	p.	PROPN
ejpam-5846	154	6	ponarin	ponarin	PROPN
ejpam-5846	154	7	.	.	PUNCT
ejpam-5846	155	1	elementary	elementary	ADJ
ejpam-5846	155	2	geometry	geometry	PROPN
ejpam-5846	155	3	,	,	PUNCT
ejpam-5846	155	4	volume	volume	NOUN
ejpam-5846	155	5	1	1	NUM
ejpam-5846	155	6	.	.	PUNCT
ejpam-5846	155	7	mtsnmo	mtsnmo	PROPN
ejpam-5846	155	8	,	,	PUNCT
ejpam-5846	155	9	moscow	moscow	PROPN
ejpam-5846	155	10	,	,	PUNCT
ejpam-5846	155	11	2008	2008	NUM
ejpam-5846	155	12	.	.	PUNCT
ejpam-5846	156	1	(	(	PUNCT
ejpam-5846	156	2	in	in	ADP
ejpam-5846	156	3	russian	russian	NOUN
ejpam-5846	156	4	)	)	PUNCT
ejpam-5846	156	5	.	.	PUNCT
ejpam-5846	157	1	[	[	X
ejpam-5846	157	2	10	10	NUM
ejpam-5846	157	3	]	]	X
ejpam-5846	157	4	michael	michael	PROPN
ejpam-5846	157	5	serra	serra	PROPN
ejpam-5846	157	6	.	.	PUNCT
ejpam-5846	158	1	discovering	discover	VERB
ejpam-5846	158	2	geometry	geometry	NOUN
ejpam-5846	158	3	an	an	DET
ejpam-5846	158	4	investigative	investigative	ADJ
ejpam-5846	158	5	approach	approach	NOUN
ejpam-5846	158	6	.	.	PUNCT
ejpam-5846	159	1	key	key	ADJ
ejpam-5846	159	2	curriculum	curriculum	PROPN
ejpam-5846	159	3	press	press	NOUN
ejpam-5846	159	4	,	,	PUNCT
ejpam-5846	159	5	2003	2003	NUM
ejpam-5846	159	6	.	.	PUNCT
ejpam-5846	160	1	[	[	X
ejpam-5846	160	2	11	11	NUM
ejpam-5846	160	3	]	]	X
ejpam-5846	160	4	i.	i.	PROPN
ejpam-5846	160	5	f.	f.	PROPN
ejpam-5846	160	6	sharigin	sharigin	PROPN
ejpam-5846	160	7	.	.	PUNCT
ejpam-5846	161	1	elementary	elementary	ADJ
ejpam-5846	161	2	geometry	geometry	PROPN
ejpam-5846	161	3	,	,	PUNCT
ejpam-5846	161	4	volume	volume	NOUN
ejpam-5846	161	5	1	1	NUM
ejpam-5846	161	6	.	.	PUNCT
ejpam-5846	162	1	drofa	drofa	NOUN
ejpam-5846	162	2	,	,	PUNCT
ejpam-5846	162	3	moscow	moscow	PROPN
ejpam-5846	162	4	,	,	PUNCT
ejpam-5846	162	5	1999	1999	NUM
ejpam-5846	162	6	.	.	PUNCT
ejpam-5846	163	1	(	(	PUNCT
ejpam-5846	163	2	in	in	ADP
ejpam-5846	163	3	russian	russian	NOUN
ejpam-5846	163	4	)	)	PUNCT
ejpam-5846	163	5	.	.	PUNCT
ejpam-5846	164	1	s.	s.	PROPN
ejpam-5846	164	2	j.	j.	PROPN
ejpam-5846	164	3	aliyev	aliyev	PROPN
ejpam-5846	164	4	,	,	PUNCT
ejpam-5846	164	5	m.	m.	PROPN
ejpam-5846	164	6	n.	n.	PROPN
ejpam-5846	164	7	heydarova	heydarova	PROPN
ejpam-5846	164	8	,	,	PUNCT
ejpam-5846	164	9	a.	a.	NOUN
ejpam-5846	164	10	m.	m.	PROPN
ejpam-5846	164	11	seyidova	seyidova	PROPN
ejpam-5846	164	12	/	/	SYM
ejpam-5846	164	13	eur	eur	PROPN
ejpam-5846	164	14	.	.	PUNCT
ejpam-5846	165	1	j.	j.	PROPN
ejpam-5846	165	2	pure	pure	PROPN
ejpam-5846	165	3	appl	appl	PROPN
ejpam-5846	165	4	.	.	PROPN
ejpam-5846	165	5	math	math	PROPN
ejpam-5846	165	6	,	,	PUNCT
ejpam-5846	165	7	18	18	NUM
ejpam-5846	165	8	(	(	PUNCT
ejpam-5846	165	9	1	1	NUM
ejpam-5846	165	10	)	)	PUNCT
ejpam-5846	165	11	(	(	PUNCT
ejpam-5846	165	12	2025	2025	NUM
ejpam-5846	165	13	)	)	PUNCT
ejpam-5846	165	14	,	,	PUNCT
ejpam-5846	165	15	5846	5846	NUM
ejpam-5846	165	16	9	9	NUM
ejpam-5846	165	17	of	of	ADP
ejpam-5846	165	18	9	9	NUM
ejpam-5846	165	19	[	[	SYM
ejpam-5846	165	20	12	12	NUM
ejpam-5846	165	21	]	]	X
ejpam-5846	165	22	hung	hung	PROPN
ejpam-5846	165	23	-	-	PUNCT
ejpam-5846	165	24	hsi	hsi	PROPN
ejpam-5846	165	25	wu	wu	PROPN
ejpam-5846	165	26	.	.	PUNCT
ejpam-5846	166	1	teaching	teach	VERB
ejpam-5846	166	2	geometry	geometry	NOUN
ejpam-5846	166	3	in	in	ADP
ejpam-5846	166	4	grade	grade	NOUN
ejpam-5846	166	5	8	8	NUM
ejpam-5846	166	6	and	and	CCONJ
ejpam-5846	166	7	high	high	ADJ
ejpam-5846	166	8	school	school	NOUN
ejpam-5846	166	9	according	accord	VERB
ejpam-5846	166	10	to	to	ADP
ejpam-5846	166	11	the	the	DET
ejpam-5846	166	12	common	common	ADJ
ejpam-5846	166	13	core	core	NOUN
ejpam-5846	166	14	standards	standard	NOUN
ejpam-5846	166	15	.	.	PUNCT
ejpam-5846	167	1	2013	2013	NUM
ejpam-5846	167	2	.	.	PUNCT