Question

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

Answer 1

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Answer 2

Heya friend,


Here is your answer,


Given :
ABCD is a parallelogram. Now 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)

Now,
In ΔADE and ΔBCF,

AD = BC [Using equation (1)]

DE = CF [Using equation (2)]

EA = FB [Using equation (3)]

Thus,
ΔADE ≅ BCF (SSS congruence rule)

Therefore,

Area (ΔADE) = Area (ΔBCF) (hence proved)


Hope it helps you.
Thank you.