P is any point on the diagonal BD of the parallelogram ABCD. Prove that ar`(triangleAPD)` = ar`(triangleCPD)`.

In the figure, P is a point in the interior of a parallelogram ABCD. Show that (i) ar (triangleAPB)+ar(trianglePCD=1/2ar(ABCD) (ii) ar (triangleAPD)+ar(trianglePBC)=ar(triangleAPB)+ar(trianglePCD)

O is any point on the diagonal PR of a parallelogram PQRS (figure). Prove that ar (DeltaPSO) = ar (DeltaPQO) .

O is the any point on diagonal PR of parallelogram PQRS.Prove that Ar(PSO)=Ar(PQO)

O' is any point on diagonal AC of a parallelogram ABCD. Prove that : area of Delta AOD = " area of " Delta AOB

If P is any point in the interior of a parallelogram ABCD, then prove that area of the triangle APB is less than half the are of 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.

In the adjoining figure, P is the point in the interior of a parallelogram ABCD.Show that ar(DeltaAPB) ar(DeltaPCD) =1/2ar(||gm ABCD)

In the adjoining figure, ABCD is a parallelogram and P is any points on BC. Prove that ar(triangleABP)+ar(triangleDPC)=ar(trianglePDA) .

In the adjacent figure P is a point inside the parallelogram ABCD. Prove that ar (APB) + ar (PCD) = 1/(2) ar (ABCD)

In the adjacent figure P is a point inside the parallelogram ABCD. Prove that ar (APD) + ar (PBC) = ar (APB) + ar (PCD)