Question

PQR is an isosceles triangle in which pc=pr m and n are points on PQ and PR such that angle MQR =angle NQR Prove that triangle QNR and RMQ are congruent

Answer 1

We are given that triangle PQR is an isosceles triangle in which PQ = PR .

Since the base angles of an isosceles triangle are equal,

angle PQR = angle PRQ

Also, And we are given that

angle MRQ = angle NQR

In ΔQNR and ΔRMQ

∠NQR=∠MRQ (given)

QR = QR (common)

-triangles QNR is congruent to triangles RMQ - ASA - angle side angle