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.

In a cyclic quadrilateral ABCD the diagonal AC bisects the angle BCD. Prove that the diagonal BD is parallel to the tangent to the circle at point A.

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.

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

In quadrilateral ABCD, diagonals AC and BD intersect at point E such that AE : EC = BE : ED . Show that : ABCD is a trapezium.

In the adjoining figure, ABCD is a quadrilateral in which AD ||BC . AC and BD intersect each other at point 'O'. Prove that: area of Delta COD = " area of " Delta ABO

A quadrilateral A B C D is such that diagonal B D divides its area in two equal parts. Prove that B D bisects A C . GIVEN : A quadrilateral A B C D in which diagonal B D bisects it. i.e. a r(triangle A B D)=a r(triangle B D C) CONSTRUCTION : Join A C Suppose A C and B D intersect at O . Draw A M_|_B D and C N _|_ B D . TO PROVE : A O=O C .

A quadrilateral A B C D is such that diagonal B D divides its area in two equal parts. Prove that B D bisects A C GIVEN : A quadrilateral A B C D in which diagonal B D bisects it. i.e. a r( triangle A B D)=a r( triangle B D C) CONSTRUCTION : Join A C Suppose A C and B D intersect at O . Draw A L_|_B D . TO PROVE : A O=O C

Prove that the diagonals of a rectangle bisect each other and are equal.

The diagonal AC of a quadrilateral ABCD divides it into two triangles of equal areas. Prove that diagonal AC bisects the diagonal BD.