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Question -

In the given figure, ABCD, ABFE and CDEF are parallelograms. Prove that
ar(Δ ADE) = ar(Δ BCF)



Answer -

Given:
(1) ABCD is a parallelogram,
(2) ABFE is a parallelogram
(3) CDEF is a parallelogram
To prove: Area of ΔADE = Area of ΔBCF
Proof:
We know that,” opposite sides of a parallelogram are equal”
Therefore for
Parallelogram ABCD, AD = BC
Parallelogram ABFE, AE = BF
Parallelogram CDEF, DE = CF.
Thus, in ΔADE and ΔBCF, we have
 
So be SSS criterion we have
 
This means that  
Hence it is proved that  

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