Question

Triangles ABC and PQR are both isosceles with AB = AC and PO = PR respectively. If also, AB = PQ and BC = QR, are the two triangles congruent? Which condition do you use?

It ∠B = 50°, what is the measure of ∠R?

Answer 1

Given that AB = AC in isosceles ΔABC

And PQ = PR in isosceles ΔPQR.

Also given that AB = PQ and QR = BC.

Therefore, AC = PR (AB = AC, PQ = PR and AB = PQ)

Hence, ΔABC ≅ ΔPQR

Now

∠ABC = ∠PQR (Since triangles are congruent)

However, ΔPQR is isosceles.

Therefore, ∠PRQ = ∠PQR = ∠ABC = 50°