NCERT, Class-9th, Exercise-7.3,Triangles, All Formulae & Rules for Triangles Class 9 (Quick Revision)
Q. 1. Δ ABC and Δ DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at P, show that;
(i) Δ ABD is congruent to ΔACD.
(ii) ΔABP is congruent to ΔACP.
(iii) AP bisects angle A as well as angle D.
(iv) AP is the perpendicular bisector of BC.
Q. 2. AD is an altitude of an isosceles triangle ΔABC in which AB = AC. Show that:
(i) AD bisects BC
(ii) AD bisects angle A
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 triangle PQR as shown in figure. Show that:
(i) ΔABM is congruent to Δ PQN.
(ii) ΔABC is congruent to ΔPQR.
Q. 4. BE and CF are two altitudes of a triangle ABC. Using RHS congruence rule, prove that the triangle ABC is isosceles.
Q. 5. ABC is an isosceles triangle with AB = AC. Draw AP⊥BC to show that ∠B = ∠C.
