The vertex A of `triangle ABC` is joined to a point D on the side BC. The midpoint of AD is E.
Prove that `ar(triangleBEC)=(1)/(2)ar(triangleABC)`.

ABC is a triangle in which D is the midpoint of BC and E is the midpoint of AD. Prove that ar(triangleBED)=(1)/(4)ar(triangleABC) .

D is the midpoint of side BC of triangleABC and E is the midpoint of BD. If O is the midpoint of AE, prove that ar(triangleBOE)=(1)/(8)ar(triangleABC) .

In triangleABC , point D lies on side BC. E is the midpoint of AD. Prove that, ar(EBC)= 1/2 ar(ABC)

ABC is a triangle in which D is the mid-point of BC and E is the mid-point of AD. Prove that: ar(triangleBED) = 1/4 ar(triangleABC)

In a triangle ABC, E is the mid-point of median AD. Show that ar (triangleBED)=1/4 ar( triangleABC ).

D,E and F are mid-points of the sides BC, CA and AB respectively of triangleABC . Prove that ar(triangleDEF) = 1/4 ar (triangleABC)

In the adjoining figure, BD||CA, E is the midpoint of CA and BD =(1)/(2) CA . Prove that ar(triangleABC)=2ar(triangleDBC) .

In triangleABC , AD is a median . E is the midpoint of AD and F is the midpoint of AE. Prove that ar(ABF)= 1/8 ar(ABC).

D,E and F are mid-points of the sides BC, CA and AB respectively of triangleABC . Prove that ar(||gmBDEF)= 1/2 ar (triangleABC)

triangleABC and triangleDBC are two triangles on the same base BC. A and D lies on opposite sides of BC. Prove that (ar(triangleABC))/(ar(triangleDBC))= (AO)/(DO)