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In the following figure, ABCD, DCFE and ABFE are parallelograms. Show that ar (ADE) = ar (BCF).

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#### Solution

It is given that ABCD is a parallelogram. We know that opposite sides of a parallelogram are equal.

∴ AD = BC ... (1)

Similarly, for parallelograms DCEF and ABFE, it can be proved that

DE = CF ... (2)

And, EA = FB ... (3)

In ΔADE and ΔBCF,

AD = BC ................[Using equation (1)]

DE = CF ................[Using equation (2)]

EA = FB ................[Using equation (3)]

∴ ΔADE ≅ BCF (SSS congruence rule)

⇒ Area (ΔADE) = Area (ΔBCF)

Concept: Theorem: Parallelograms on the Same Base and Between the Same Parallels.

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