X and Y are the mid-points of the opposite sides AB and DC of a parallelogram ABCD. Prove that `squareAXCY` is a parallelogram.

X and Y are the mid-points of the opposite sides AB and DC of a parallelogram ABCD. Then squareAXCY is a ?

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

E is the mid-point of side AB and F is the mid point of side DC of parallelogram ABCD . Prove that AEFD is a parallelogram.

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

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

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

P and Q are the mid-point of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PQRS is a parallelogram.

E and F are the mid-points of the sides AB and CD of a parallelogram ABCD. Prove that the line segment AF and CE trisects BD in three equal parts.

L and M are the mid-points of sides AB and DC respectively of parallelogram ABCD. Prove that segments DL and BM trisect diagonal AC.

P,Q are the mid points of the opposite side AB and CD of a parallelogram ABCD. AP intersects DP at S and BQ intersects CP at P. Show that PQRS is a parallelogram.