Question

In figure, ABCD is a parallelogram, P and Q are midpoints of side AB and DC respectively, then prove APCQ is a parallelogram

Answer 1

ABCD is a parallelogram ,
$AB\cong CD\text{and}AB||CD$
P and Q are the mid points of AB and CD respectively.
$\text{So,}AP\cong CQ\text{and}AP||CQ$
Thus, APCQ is also a parallelogram.