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).`

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

ABCD is a trapezium in which AB||DC and its diagonal intersect each other at point 'O'. Show that (AO)/(BO)=(CO)/(DO) .

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.

ABCD is a trapezium in which AB|\|DC and its diagonals intersect each other at point ‘O’. Show that (AO)/(BO)=(CO)/(DO) .

In the adjacent figure, triangle ABC and triangle DBC are on the same base BC. If AD and BC intersect at O, Prove that (area of triangle ABC )/(area of triangle DBC) = (AO) /(DO)

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)

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 diagonal of a trapezium ABCD in which AB////CD intersect at'O' . IF AB=2CD then the ratio of areas of triangles AOB and COD is……….

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).