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

Answer:

in triangle MRQ and triangle QNR

QR=QR(common side)

angleMRQ=angleNQR(given)

angle MQR=angleNRQ(In isosceles triangle,PQ=PR)

(if opposite sides are equal then opposite angles are equal)

triangle MRQ=~triangle QNR(by ASA congruence)