Question

Triangles ABC and PQR are both isosceles with AB = AC and PQ = PR respectively. If also, AB = PQ and BC = QR, are the two triangles congruent? Which condition do you use? IF $\angle B=50°$, what is the measure of $\angle R$?

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, $\Delta ABC\simeq \Delta PQR$

Now

$\angle ABC=\angle PQR$ (Since triangles are congruent)

However, ΔPQR is isosceles.

Therefore, $\angle PRQ=\angle PQR=\angle ABC=50°$