Question

In the given figure BC is parallel to DE. Prove that: area ∆ABE = area ∆ACD

Answer 1

=The given figure BC is parallel to

=DE.

=∆ABC and ∆BCD

=are the same parallel lines BC and =DE

=ABCD=∆BCE+∆ABC

=∆ACD=∆ABE

:hence prove

Answer 2

Area of ∆ABE = Area of ∆ACD

Explanation:

Given that BC is parallel to DE.

BC//DE

Area of ∆CBE = Area of ∆CBD ----------(1)

Reason: Triangles on the same base and between the same parallels are equal in area.

Area of ∆ABE = Area of ∆ABC + Area of ∆CBE

= Area of ∆ABC + Area of ∆CBD, Substituting from equation (1)

From the figure, we get that  ∆ABC + ∆CBD = ∆ACD.

So Area of ∆ABE = Area of ∆ACD

Thus proved.