NCERT Solutions Class 9 Maths Chapter 7 – Triangles Exercise 7.3

Chapter 7 – Triangles Exercise 7.3

(Q 1) ∆ ABC and ∆DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC (see Fig. 7.39). If AD is extended to intersect BC at P, show that
(i) ∆ABD≅ ∆ACD
(ii) ∆ABP≅ ∆ACP
(iii) AP bisects ∠ A as well as ∠ D
(iv) AP is the perpendicular bisector of BC .

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(Q 2) AD is an altitude of an isosceles triangle ABC in which AB = AC. Show that
(i) AD bisects BC
(ii) AD bisects ∠A

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(Q 3) Two sides AB and BC and median AM of one triangle ABC are respectively equal to sides PQ and QR and median PN of ∆ PQR (see Fig. 7.40). Show that:
(i) ∆ABM≅ ∆PQN
(ii) ∆ABC≅ ∆PQR

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(Q 4) BE and CF are two equal altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.

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(Q 5) ABC is an isosceles triangle with AB = AC. Draw AP⊥BC to show that ∠B = ∠C.

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