Q15 of 25 Page 9

In Fig., ABCD and AEFD are two parallelograms. Prove that ar(Δ PEA) = ar(Δ QFD).

Proof:


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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