Q. 155.0( 6 Votes )
In Fig., ABCD and AEFD are two parallelograms. Prove that ar(Δ PEA) = ar(Δ QFD).
In triangles PEA and QFD, we have
∠APE = ∠DQF (Corresponding angles)
AE = DF (Opposite sides of II" AEFD)
∠AEP = ∠DFQ (Corresponding angles)
∴ △PEA ≅ △QFD (AAS congruence criterion)
As congruent triangles have equal area.
∴ ar (△PEA) ≅ ar (△QFD)
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