In the trapezium ABCD, AB || DC. The diagonals AC and BD of it intersects each other at O. Prove that `DeltaAOD=DeltaBOC.`

ABCD is a parallelogram. The diagonals AC and BD intersect each other at ‘O’. Prove that ar(DeltaAOD) = ar(DeltaBOC) . (Hint: Congruent figures have equal area)

In the figure, diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar(DeltaAOD) = ar(Delta BOC).

The diagonals AC and BD of a quadrilateral ABCD intersects each other at O such that DeltaAOD=DeltaBOC . Prove that ABCD is trapezium.

In trapezium ABCD , BC||AD and AD=4cm . The two diagonals AC and BD intersect at the point O in such a way that (AO)/(OC)=(DO)/(OB)=(1)/(2) . Find the length of BC .

In a trapezium ABCD, BC AD and AD = 4 cm. the two diagonals AC and BD intersect at the point O in such a way that AO/OC = DO/OB = 1/2. Calculate the length of BC.

B is a vertex of the isosceles triangle ABC. D and E are the mid-points of AB and AC. If BE and CD intersects each other at F prove that DeltaBDE=3DeltaDEF .

Kamala have drawn a trapezium PQRS of which PQ||SR . If the diagonals PR and QS intersect each other at O , then prove that OP:OR=OQ:OS , If SR=2PQ , then prove that O is a point of trisection of both the diagonals.

In a quadrillateral ABCD, it is given that AB ||CD and the diagonals AC and BD are perpendiclar to each other . Show that AD. BC = AB. CD.

P is any point on the diagonal BD of the parallelogram ABCD. Prove that DeltaAPD=DeltaCPD .

In the quadrilateral ABCD, the diagonals AC and BD are equal and perpendicular to each other. What type of a quadrilateral is ABCD?