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.
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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