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

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.

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

PQRS is cyclic quadrilateral. Extended PQ and SR intersect each other at A . Prove that AP.AQ=AR.AS .

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

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

ABCD is a parallelogram. AC and BD are the diagonals intersect at O. P and Q are the points of tri section of the diagonal BD. Prove that CQ" ||" AP and also AC bisects PQ (see figure).

If the diagonals of the quadrilateral ABCD intersect each other orthogonally,then prove that AB^(2) + CD^(2) = BC^(2) + DA^(2)

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.