If `P\ a n d\ Q` are the mid points of the sides AB and CD of a parallelogram ABCD, prove that DP and BQ respectively.

If P\ a n d\ Q are the mid points of the sides AB and CD of a parallelogram ABCD, prove that DP and BQ cut the diagonal AC in its points of trisection which are also the points of trisection of DP and BQ respectively.

If P and Q are the middle points of the sides BC and CD of the parallelogram ABCD, then AP+AQ is equal to

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.

P and Q are the mid-point of the oposite sides AB and CD of a parallelogram ABCD. AQ interects DP at S and BQ interects CP at R. Show that PQRS 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 middle points of the parallel sides AB and CD of a parallelogram ABCD are P and Q respectively. If AQ and CP divide the diagonal BD into three parts BX, XY and YD, then which one of the following is correct ?

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

ABCD is a parallelogram. L and M are respectively mid points of sides AB and DC. Prove that LD and MB trisects diagonals AC.

P, Q , R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD in which AC = BD. Prove that PQRS is a rhombus.