Question

HELP PLEASE == PGR is an isosceles triangle in which PQ=PR

M and N are points on PQ and PR such that angle MRQ and angle NQR.
Prove that triangles QNR and RMQ are congruent

Answer 1

Angle NQR congruent to Angle MRQ because it is given

Side QR is congruent to side QR because they are the same side

Angle NRQ is congruent to angle MQR because they are the equal angles of an isosceles triangle

Triangle QNR is congruent to Triangle RMQ by ASA

Explanation:

It's actually pretty simple. first you should be able to know angles NRQ and MQR are congruent because triangle PQR is isosceles . So now if you look at the two other triangles you can say angle NQR is congruent to angle MRQ, because of the information given, and with wht I just explained angles NRQ and MQR are congruent. So now you can say the two triangles are similar by the angle angle postulate.

To Say they are congruent since QR is the same for both triangles you can use the ASA postulate