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In figure, ABCD and AEFD are two paralle...

In figure, ABCD and AEFD are two parallelograms. Prove that `ar (DeltaPEA) = ar (DeltaQFD)`.

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Given: ABCD and AEFD are two parallelograms.
To prove : `ar(Delta PEA) = ar(Delta QFD)`
Consturction : Join PD.
Proof: In `Delta PEA and Delta QFD`,
`:'{(angleAPE = angleDQF,( :' " corresponding angles are equal as " AB||CD)),(angleAEP = angleDFQ,( :' "corresponding angles are equal as " AE||DF)),(" "AE = DF,( :' " opposite sides of a parallelogram are equal")):}`
`:. Delta PEA ~= Delta QFD` (by AAS congruence rule)
Hence, `ar(Delta PEA) = ar (Delta QFD)` ( `:'` congruent triangles have equal aras)
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