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 triangles, show that (OA)/(OC) = (OB)/(OD) .

In the given figure AB and CD bisect each other at O. Prove that AC = BD.

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

In the given figure, two chords AB and CD intersect each other at the point P. Prove that DeltaAPC ~ DeltaDPB

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

ABCD is a trapezium in which AB||DC and its diagonals intersects each other at the point O. Show that (AO)/(BO)=(CO)/(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)

In the given figure, if AC = BD, then prove that AB = CD.