Question

In the given figure, D is mid-point of side AB of ΔABC and BDEC is a parallelogram.

Prove that: Area of ABC = Area of // gm BDEC.

Answer 1

Here AD = DB and EC = DB, therefore EC = AD
Again, 
∠EFC = ∠AFD         .....( Opposite angles )

Since ED and CB are parallel lines and AC cut this line, therefore
∠ECF = ∠FAD 
From the above conditions, we have
ΔEFC = ΔAFD
Adding quadrilateral CBDF in both sides, we have
Area of // gm BDEC = Area of ΔABC.