Question

7. In Fig. 7, PQR is a triangle in which PM is the bisector of angle p and PM perpendicular QR. Prove the
(1)∆PMQ ~∆PMR
(ii) QM = MR​

Answer 1

Answer:

According to the question :-

PM is perpendicular to QR so,

<PMQ=<PMR=90°

And, as PM is bisector of angle p

So,

<QPM=<RPM=½<QPR

Also, PM is the common side for both triangles

So, ∆PQM is congruent to ∆PRM (by ASA property)

As, ∆PQM≈∆PRM

so, QM=MR