Question

in the adjoining figure ABCD IS A parallelogram.IF P AND Q ARE POINTS ON AD AND BC RESPECTIVELY SUCH THAT AP=AD÷3 AND CQ=BC÷3,PROVE THAT AQCP IS A PARALLELOGRAM

Answer 1

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Answer 2

Parallelogram = ABCD  (Given)

AP =AD/3 (Given)

CQ = BC/3 (Given)

Therefore,

= AD = BC (Opposite sides of a parallelogram )

Thus, AD || BC

AP = 1/3 AD --- equation (1)

CQ = 1/3 BC

CQ = 1/3 AD ---equation (2) ( Since, AD= BC)

Thus, from equation 1 and 2

= AP = CQ

= AP || CQ  (As, a part of equal and parallel sides are also equal and parallel )

Hence, AQCP is a parallelogram