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ABCD is a parallelogram. P is a point on AD such that AP = \(\frac{1}{3}\) AD and Q is a point on BC such that CQ = \(\frac{1}{3}\) BC. Prove that AQCP is a parallelogram.

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ABCD is a parallelogram 

⇒ AD = BC and AD || BC 

\(\frac{1}{3}\) AD = \(\frac{1}{3}\) BC and AD || BC 

⇒ AP = CQ and AP || CQ 

⇒ APCQ is a parallelogram.

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