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Question
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)
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