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 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)

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 .

DeltaABC and DeltaDBC are two isosceles triangles on thesame base BC (see figure). Show that /_ ABD = /_ ACD.

In the figure, ΔABC, D, E, F are the midpoints of sides BC, CA and AB respectively. Show that (i) BDEF is a parallelogram (ii) ar(DeltaDEF)=1/4ar(DeltaABC) (iii) ar(BDEF)=1/2ar(DeltaABC)

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).

In a triangle ABC (see figure), E is the midpoint of median AD, show that (i) ar DeltaABE = ar DeltaACE (ii) ar DeltaABE=1/4ar(DeltaABC)

Two triangles ABC and ABD of equal areas are on the opposite sides of AB. Prove that AB bisects CD equally.