Question

PQR is an isosceles triangle in which PQ=PR
M and N are points on PQ and PR such that angle MRQ=angle NQR

Prove that triangles QNR and RMQ are congruent

Answer 1

9514 1404 393

Explanation:

∠MRQ ≅ ∠NQR . . . . given

QR ≅ RQ . . . . reflexive property

∠PQR ≅ ∠PRQ . . . . property of isosceles triangle PQR

ΔQNR ≅ Δ RMQ . . . . ASA postulate