Question

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

Answer 1

Answer:

ABCD is a parallelogram.

AD=BC and AD∥BC.

3

1

AD=

3

1

BC and AD∥BC.

AP=CQ and AP∥CQ.

Thus, APCQ is a parallelogram such that one pair of opposite side AP and CQ are parallel and equal.

Hence, APCQ is a parallelogram.