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).`

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

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

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)

Diagonals of a trapezium ABCD with AB || DC, intersect each other at the point ‘O’. If AB = 2CD, find the ratio of areas of triangles AOB and COD.

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 .

The diagonals of the square ABCD intersect each other at O .Let OPbotAB is constructed. Prove that angleAOP =anglePBO

In the figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that (i) ar (DeltaACB) = ar (DeltaACF) (ii) ar (AEDF) = ar (ABCDE)

Two perpendicular BD and CE are drawn from the vertices B and C respectively on the sides AC and AB of the Delta ABC ,which intersect each other at the point P. Prove that AC^(2) + BP^(2) = AB^(2) + CP^(2)

The diagonals of a quadrilateral ABCD intersect each other at point ‘O’ such that (AO)/(BO) = (CO)/(DO) . Prove that ABCD is a trapezium

The diagonals AC and BD of the parallelogram ABCD intersect each other at O . Any straight line passing through O intesects the sides AB and CD at the points P and Q respectively . Prove that OP = OQ.