Question

in fig prove that PL=QM
LO=OM​

Answer 1

Answer:

In triangle POQ,

angle OPQ = angle OQP

Therefore, OP= OQ (Sides opposite to equal angles are equal)

Also, angle LOP = angle OPQ and angle MOQ = angle OQP

(LM II PQ and they are pair of alternate interior angles)

Now in triangles LOP and MOQ,

OP=OQ

angle LPO = angle MQO

angle LOP = angle MOQ (Proved above)

By ASA congruency rule, triangle LOP is congruent to triangle MOQ.

PL = QM and LO = OM (CPCT)

Hence Proved

HOPE IT HELPS !