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In a parallelogram ABCD, P is a point on side AD such that 3AP = AD and Q is a point on BC such that 3CQ = BC. Prove that : AQCP is a parallelogram.

Rectilinear Figures

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Answer

In a parallelogram ABCD, P is a point on side AD such that 3AP = AD and Q is a point on BC such that 3CQ = BC. Prove that : AQCP is a parallelogram. Chapterwise Revision (Stage 1), Concise Mathematics Solutions ICSE Class 9.

Given: ABCD is a parallelogram.

AD = BC (Opposite sides of a parallelogram are equal)

⇒ 3AP = 3CQ

⇒ AP = CQ

AD ∥ CB (Opposite sides of a parallelogram are parallel)

⇒ AP ∥ CQ

Opposite sides AP and CQ are parallel and equal.

Hence, AQCP is a parallelogram.

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