Q. 64.5( 15 Votes )

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.

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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