Diagonal AC of a parallelogram ABCD bisects A. Show that
ABCD is a rhombus.

Diagonal AC of a parallelogram ABCD bisects A. Show that it bisects C also

Diagonals AC of a parallelogram ABCD bisects angleA . Show that it bisects angleC also ABCD is a rhombus

The diagonal AC of a parallelogram ABCD intersects DP at the point Q, where ‘P’ is any point on side AB. Prove that CQ xx PQ = QA xx QD .

The diagonal BD of parallelogram ABCD intersect AE at F as shown in the figure. If E is any point on BC, then prove that DFxxEF=FB=FA .

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram , ABCD . Show that ar(APB) = ar (BQC)

If the diagonals of a parallelogram are equal, then show that it is rectangle .

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD. Show that ar (APB) = ar (BQC).

Diagonals AC and BD of a quadrilateral ABCD each other at P. Show that ar (APB) xx ar (CPD) =ar (APD) xx ar (BPC)

In P is a point in the interior of a parallelogram ABCD. Show that (ii) ar (APD) + ar (PBC) = ar (APB) + ar (PCD)

IN the figure, P is a point in the interior of a parallelogram ABCD. Show that (i) ar(APB) + ar(PCD) = 1/2 ar (ABCD) (ii) ar (APD) + ar(PBC) = ar(APB) + ar (PCD)