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

  

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

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Given,

ABCD, DCFE and ABFE are parallelograms

To prove,

ar (△ADE) = ar (△BCF)

Proof:

In △ADE and △BCF

AD = BC [Since, they are the opposite sides of the parallelogram ABCD]

DE = CF [Since, they are the opposite sides of the parallelogram DCFE]

AE = BF [Since, they are the opposite sides of the parallelogram ABFE]

△ADE ≅ △BCF [Using SSS Congruence theorem]

ar(△ADE) = ar(△BCF) [ By CPCT]

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