In Fig. 9.31, ABCD, DCFE and ABFE are parallelograms. Show that `a r ( – InterviewSolution

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1.	In Fig. 9.31, ABCD, DCFE and ABFE are parallelograms. Show that `a r (A D E) = a r(B C F)dot`
Answer» In parallelogram, `ABCD`, `AD = BC` In parallelogram, `DCFE`, `DE = CF` In parallelogram, `ABFE`, `AE = AF` Now, in `Delta ADE` and `Delta BCF` `AD = BC` `DE = CF` `AE = AF` So, from SSS criterion, `Delta ADE ~= Delta BCF` As these two triangles are congruent, their areas will be equal. `ar(ADE) = ar(BCF)`

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