P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O.

Question

Philoid · Accepted Answer

Given, ABCD is a parallelogram whose diagonals bisect each other at O.

Now, in ΔODP and ΔOBQ,

∠BOQ = ∠POD

∠OBQ = ∠ODP (AD||BC and BD is transversal)

OB = OD

OP = OQ

Hence, O bisect PQ.