In the figure, ΔABC and ΔABD are two triangles on the same base AB. If line segment CD is bisected by `bar(AB)` at O, show that ar `(DeltaABC) = ar (DeltaABD).`

In the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that (ar(ABC))/(ar(DBC))= (AO)/(DO) .

In the given figure, ABC and DBC are two triangles on the same base BC. Prove that (ar(ABC))/(ar(DBC))= (AO)/(DO) .

In the adjacent figure DeltaABC and DeltaDBC are two triangles such that bar(AB) = bar(BD) and bar(AC) = bar(CD) . Show that DeltaABC ~= DeltaDBC.

Triangle ABC and parallelogram ABEF are on the same base, AB as in between the same parallels AB and EF. Prove that ar (DeltaABC) = 1/2 ar(|| gm ABEF)

ABC and DBC are two isosceles triangles on the same base BC (see the given figure). Show that angle ABD = angle ACD .

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

AD and BC are equal and perpendiculars to a line segment AB. Show that CD bisects AB.

In the figure D, E are points on the sides AB and AC respectively of DeltaABC such that ar(DeltaDBC) = ar(DeltaEBC) . Prove that DE || BC.

In the given figure, AB||DC and AD||BC show that DeltaABC ~= Delta CDA .

In the given figure, AB and DC are both perpendicular to line segment AD. BC intersects AD at P and P is the midpoint of AD. Prove that, ( 1 ) AB = CD ( 2 ) P is the midpoint of BC.