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 ∠B = 50°, what is the measure of ∠R?

Answer 1

We have AB = AC in isosceles $△$ABC
and PQ = PR in isosceles $△$PQR.
Also, we are given that AB = PQ and QR = BC.

Therefore, AC = PR (AB = AC, PQ = PR and AB = PQ)​
Hence, $△\text{ABC}\cong △\text{PQR}$.
Now
$$\begin{gathered} \angle \mathrm{ABC}=\angle \mathrm{PQR}(\mathrm{Since}\mathrm{triangles}\mathrm{are}\mathrm{congruent}) \\ \text{However, △PQR is isosceles.} \\ \text{Therefore, ∠PRQ =∠PQR =∠ABC}=50° \end{gathered}$$