In the given figure; AD is median of △ ABC and E is any point on median AD. Prove that Area (△ ABE) = Area (△ ACE).

We know that,

Median of a triangle divides it into two triangles of equal area.

Given,

AD is the median of △ ABC.

∴ Area of △ ABD = Area of △ ACD ……….(1)

Since, E is a point on median AD.

∴ ED is median of △ EBC.

∴ Area of △ EBD = Area of △ ECD ……….(2)

Subtracting equation (2) from (1), we get :

⇒ Area of △ ABD - Area of △ EBD = Area of △ ACD - Area of △ ECD

⇒ Area of △ ABE = Area of △ ACE.

Hence, proved that area (△ ABE) = area (△ ACE).