ABCD and APCR are the two parallelograms and AC is the common diagonal. Prove that PBRD is a parallelogram.

In the figure ABCD and DXBY are two parallelograms with BD as the common diagonal.Prove that AYCX is also a parallelogram.

The sides AB and CD of a parallelogram ABCD are bisected at E and F. Prove that EBFD is a parallelogram.

Two segments AC and BD bisect each other at O. Prove that ABCD is a parallelogram.

ABCD and APQR are two parallelograms. Prove that /_C=/_Q and /_B=/_R

E and F are points on diagonal AC of a parallelogram ABCD such that AE=CF. Show that BFDE is a parallelogram.

In a parallelogram ABCD,points P and Q are points of trisection of diagonal BD.Prove that CQ is parallel to AP.

In parallelogram ABCD,E is the mid-point of AD and F is the mid-point of BC.Prove that BFDE is a parallelogram.

In the adjoining figure, prove that ABCD is a parallelogram. Also find its area.

Two points X and Y lie on the diagonal BD of a parallelogram ABCD such that DX = BT. Prove that squareAXCY is a parallelogram.

ABCD is a quadrilateral and BD is one of its diagonals as shown in Figure.Show that ABCD is a parallelogram and find its area.