Question

If two triangles ABC and PQR have angle A = angle P = 90 ° and AB = AC = PQ = PR, then under which criterian of congruency, they are congruent?

Answer 1

Step-by-step explanation:

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.

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Answer 2

Answer:

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Step-by-step explanation:

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.