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

Given that AB = AC in isosceles ΔABC

And PQ = PR in isosceles $\Delta$PQR.

Also given that AB = PQ and QR = BC.

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

Hence, from SSS Congruence ruke,
$\Delta ABC\cong \Delta PQR$

Now

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

However, $\Delta PQR$ is isosceles.

Therefore, $\angle PRQ=\angle PQR=\angle ABC={50}^o$