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).`

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point ‘O’. Using the criterion of similarity for two triangles, show that (OA)/(OC) = (OB)/(OD) .

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.

squareABCD is a trapezium in which AB|| DC and its diagonals intersect each other at points O . Show that AO : BO = CO : DO.

In the figure seg AC and seg BD intersects each other at point P and (AP)/(CP)=(BP)/(DP) . Then Prove that DeltaABP~DeltaCDP .

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

Attempt any Two of the following: In squareABCD ,seg AB ||seg CD . Diagonal AC and BD intersect each other at point P . Prove : (A(DeltaABP))/(A(DeltaCPD))=(AB^(2))/(CD^(2))

In the adjoining figure, two circles intersect each other at points A and E . Their common secant through E intersects the circle at points B and D . The tangents of the circles at point B and D intersect each other at point C . Prove that squareABCD is cyclic .

ABCD is trapezium with AB || DC. The diagonal AC and BD intersect at E . If Delta AED ~ Delta BEC . Prove that AD = BC .

In the figure, ABCD is a quadrilateral. AC is the diagonal and DE || AC and also DE meets BC produced at E. Show that ar(ABCD) = ar (DeltaABE).

The diagonal AC of a parallelogram ABCD intersects DP at the point Q, where ‘P’ is any point on side AB. Prove that CQ xx PQ = QA xx QD .