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