Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium.

The diagonals of a quadrilateral ABCD intersect each other at the point o Such that (AO)/(BO)=(CO)/(DO) , show that ABCD is trapezium.

Diagonals AC and BD of quadrilateral ABCD intersect each other at P. Show that ar (APB) xx ar (CPD) = ar (APD)xx ar(BPC) .

Diagonals AC and BD of quadrilateral ABCD interset at O such that OB = OD , If AB = Cd, then show that : ar(DCB) = ar(ACB)

Diagonal AC of a parallelogram ABCD bisects angleA show that ABCD is a rhombus.

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If /_DAC = 32^@ and /_AOB=70^@ , then /_DBC is equal to

The diagonal AC and BD of a rectangle ABCD intersect each other at P. if angleABD=50^@ and angleDPC =

Diagonals AC and BD of a parallelogram ABCD intersect each other at O. if OA=3 cm and OD=2 cm, determine the length of AC and BD.

The diagonals of a prallelogram ABCD intersect at O. A line through O intersets AB at P and DC at Q. prove that OP=OQ.

D and E are points on sides AB and AC respectively of DeltaABC such that ar (DBC) = ar (EBC). Prove that DE II BC .

In the quadrilateral ABCD, it is given that L is the mid-point of AC. Prove that arc(qud.ABLD)=ar(quad.DLBC)