ABCD is a parallelogram . P is a midpoint on AD such that AP=1/3AD and Q is a midpoint onBC such that CQ=1/3BC. prove that AQCP is a parallelogram.
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It is a parallelogram because diagonals of it bisects each other
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CQ = 1/3 BC
but AD = BC (opposite sides of parallelogram ABCD)
therefore , 1/3 AD = 1/3 BC (both sides of the equation are divided by 3)
so, AP = CQ (substitution) - 1
also , AP is parallel to CQ because AD is parallel to BC and A-P-D , B-Q-C (that is they are in a straight line) - 2
so by 1 and 2 , AQCP is a parallelogram (a pair of opposite sides test)
( this the full answer)