Question

l and m are two parallel lines intersected by another pair of parallel lines p and q (see Fig. 7.19). Show that △ ABC ≅ △ CDA.

AB is a line segment and P is its mid-point. D and E are points on the same side of AB such that ∠ BAD = ∠ ABE and ∠ EPA = ∠ DPB (see Fig. 7.22). Show that (i) △ DAP ≅ △ EBP (ii) AD = BE

In △ ABC, the bisector AD of ∠ A is perpendicular to side BC (see Fig. 7.27). Show that AB = AC and △ ABC is isosceles.

In triangles ABC and DEF, ∠A = ∠D, ∠B = ∠E and AB = EF. Will the two triangles be congruent? Give reasons for your answer.

In triangles ABC and PQR, ∠A = ∠Q and ∠B = ∠R. Which side of ∆ PQR should be equal to side AB of ∆ ABC so that the two triangles are congruent? Give reason for your answer.