Question

ABCD is parallelogram. P is a point on AD such that AP = 1/3 AD and Q is a point on BC such that CQ = 1/3 BC. Prove that

AQCP is a parallelogram.

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Answer 1

Answer:

Step-by-step explanation:

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)