P is the mid-point of diagonal AC of quadrilateral ABCD. Prove that the quadrilaterals ABPD and CBPD are equal in area.

In trapezium ABCD, side AB is parallel to side DC. Diagonals AC and BD intersect at point P. Prove that triangles APD and BPC are equal in area.

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

If the quadrilateral formed by joining the mid points of the adjacent sides of quadrilateral ABCD is a rectangle, show that the diagonals AC and BD intersect at right angle.

If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

The diagonals of a quadrilateral ABCD are mutually perpendicular . Prove that the quadrilateral formed by joining the mid-points of its consecutive sides is a reactangle.

In the following figure, CE is drawn parallel to diagonal DB of the quadrilateral ABCD which meets AB produced ar point E. Prove that DeltaADE and quadrilateral ABCD are equal in area.

E, F, G and H are the mid-points of the sides of a parallelogram ABCD. Show that area of quadrilateral EFGH is half of the area of parallelogram ABCD.

In quadrilateral ABCD, diagonal BD is bisected by the diagonal AC. Prove that : Delta ABC and Delta ADC are equal in area.

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

ABCD is a rhombus and P, Q, R and S are wthe mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle.