Question

In a parallelogram ABCD points P and Q are points of trisection of diagonal BD. Prove that CQ is parallel to AP

Answer 1

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Given: 

AC and BD are the diagonals of the parallelogram ABCD which intersect O. The points P and Q trisects the diagonal BD.

To prove:

 (i) CQ || AP

(ii) AC bisect PQ.

Proof:

AC and BD bisect each other at O.

OB = OD
OA = OC

P and PQ trisects the diagonal BD.

∴ DQ = PQ = BP

OB = OD
BP = DQ

∴ OB – BP = OD – DQ

⇒OP = OQ

so in Quadrilateral APCQ diagonals AC and PQ are such that OP = OQ and OA = OC

the diagonals AC and PQ bisect each other at O.

Hence, APCQ is a parallelogram.

∴ CQ || AP  



Thank you