In figure, ABCD and AEFD are two parallelograms. Prove that `ar (Delta – InterviewSolution

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1.	In figure, ABCD and AEFD are two parallelograms. Prove that `ar (DeltaPEA) = ar (DeltaQFD)`.
Answer» We have: AC = BD (opp. Sides of \|\|gm ABDC) CE = DF (opp. Sides of \|\|gm CDFE) AE = BF (opp. Sides of \|\|gm ABFE) `therefore triangleACE cong triangleBDF` [SSS-criterion]. And so, `ar(triangleACE)=ar(triangleBDF)` " " [`therefore` congruent figures have equal areas].

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