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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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:
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Step-by-step explanation:
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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