Question

ABCD is a parallelogram. If P, Q are points on the diagonal BD such that BP = PQ prove that APCQ is parallelogram
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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

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.

therefore:- DQ = PQ = BP

OB = OD

BP = DQ

therefore:- 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.

therefore:- CQ || AP