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

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

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)

In an isosceles triangle ABC, with AB=AC, the bisectors of /_B and /_C intersect each other at O. Join A to O. Show that: OB=OC

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

ABCD is a trapezium in which AB||DC the diagonals AC and BD are intersecting at E. IF DeltaAED is similar to DeltaBEC , then prove that AD=BC.

In an isosceles triangle ABC, with AB = AC, the bisectors of /_ B and /_ C intersect each other at O. Join A to O. Show that : (i) OB = OC (ii) AO bisects /_A

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) .

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.