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where ABC is an isosceles triangle in which AB = AC. P is any point in the interior of AABC such that ZABP = ZACP. Prove that (a) BP = CP %3D (b) AP bisects ZBAC.

where ABC is an isosceles triangle in which AB = AC. P is any point in the interior of AABC such that ZABP = ZACP. Prove that (a) BP = CP %3D (b) AP bisects ZBAC.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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(b) In the figure (ii) given below, AB |I CD. Find the values of x, y and z 2 (4) In the figure (i) given below MN is parallel to QR. PQ PR and ZLPN- 65 Find 1 (a) ABC is a right angled triangle in which ZA 90 and AB AC Find B and C is drawn parallel to QR intersecting PR at T. Prove that PS PT (b) PQR is a triangle in which PQ PR.S is any point on the side PQ Through S, a line Exercise 7.3 the measure of ZQPR. L. PA65° M 24° R (i) (ii) 3. In a triangle ABC, AB = AC, D and E are points on the sides AB and AC respectively such that BD = CE. Show that: (1) ADBC AECB (ii) ZDCB = ZEBC () OB = OC, where O is the point of intersection of BE and CD. *ABC is an isosceles triangle in which AB = AC. P is any point in the interior of AABC such that ZABP = ZACP. Prove that (a) BP = CP (b) AP bisects ZBAC. * in the adjoining figure, D and E are points on the side BC AABD AACE. (Exemplar) I lint. AD = AE ZADE ZAED 180°-LADE = 180°-ZAED ZADB = LAEC. AABD E AACE (SAS). 6. square ABCD. Show that (1) AADE = ABCE (Exemplar) torior of a square ABCD such that iangle (Exemplar (ii) AEB is an isosceles triangle
Transcribed Image Text:(b) In the figure (ii) given below, AB |I CD. Find the values of x, y and z 2 (4) In the figure (i) given below MN is parallel to QR. PQ PR and ZLPN- 65 Find 1 (a) ABC is a right angled triangle in which ZA 90 and AB AC Find B and C is drawn parallel to QR intersecting PR at T. Prove that PS PT (b) PQR is a triangle in which PQ PR.S is any point on the side PQ Through S, a line Exercise 7.3 the measure of ZQPR. L. PA65° M 24° R (i) (ii) 3. In a triangle ABC, AB = AC, D and E are points on the sides AB and AC respectively such that BD = CE. Show that: (1) ADBC AECB (ii) ZDCB = ZEBC () OB = OC, where O is the point of intersection of BE and CD. *ABC is an isosceles triangle in which AB = AC. P is any point in the interior of AABC such that ZABP = ZACP. Prove that (a) BP = CP (b) AP bisects ZBAC. * in the adjoining figure, D and E are points on the side BC AABD AACE. (Exemplar) I lint. AD = AE ZADE ZAED 180°-LADE = 180°-ZAED ZADB = LAEC. AABD E AACE (SAS). 6. square ABCD. Show that (1) AADE = ABCE (Exemplar) torior of a square ABCD such that iangle (Exemplar (ii) AEB is an isosceles triangle
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