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Question
P and Q are the points of trisection of the diagonal BD of a parallelogram AB Prove that CQ is parallel to AP. Prove also that AC bisects PQ.
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Solution
We know that, diagonals of a parallelogram bisect each other
∴OA = OC and OB = OD
Since P and Q are point of intersection of BD
∴BP = PQ = QD
Now, OB = OD and BP = QD
⇒ OB - BP = OD - QD
⇒ OP = OQ
Thus in quadrilateral APCQ, we have
OA = OC and OP = OQ
⇒ diagonals of quadrilateral APCQ bisect each other
∴APCQ is a parallelogram
Hence AP || CQ
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