Question

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

Answer 1

 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)

Answer 2

Answer:

 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)