P and Q are the points of trisection of the diagonal BD of a parallelogram ABCD. Prove that CQ is parallel to AP. Proves also that AC bisects PQ.

Question

Philoid · Accepted Answer

Given,

In a parallelogram ABCD

Since diagonal of parallelogram bisects each other

OA = OC and OB = OD

Since P&Q are the point of trisection of BD

BP = PQ = QD

Now, OB = OD and BP = QD

OB-BP = OD-QD

OP = OQ

Diagonals of quadrilateral bisect each other

Hence, APCQ is a parallelogram.