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in Quadrilaterals by (27.3k points)
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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.

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Best 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.

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