Question -
Answer -
Given,
ABCD, DCFE and ABFEare parallelograms
To prove,
ar (△ADE) = ar (△BCF)
Proof,
In △ADE and △BCF,
AD = BC [Since, theyare the opposite sides of the parallelogram ABCD]
DE = CF [Since, theyare the opposite sides of the parallelogram DCFE]
AE = BF [Since, theyare the opposite sides of the parallelogram ABFE]
, △ADE ≅ △BCF [Using SSS Congruence theorem]
, ar(△ADE) = ar(△BCF) [ By CPCT]