Question

In ∆ and ∆, if AB = PQ, ∠A = ∠P, ∠B = ∠Q, then which one of the congruence
conditions apply.

Answer 1

Answer:

Isosceles but not congruent

In △ABC and △PQR

∠C=∠P (Given)

∠B=∠Q (Given)

∠A=∠R (Third angle of the triangle)

Thus, △ABC∼△PQR

Also, given, AB=AC

Thus, ∠B=∠C (Isosceles triangle Property)

But, ∠B=∠Q and ∠C=∠P

Hence, ∠Q=∠P

or PR=QR

Thus, both the triangles are Isosceles but not congruent.