Question

46. In the given figure, ABCD and EFD are two
parallelograms. Which of the following statements
is correct?

I. PE=QF
II. ar(ΔAPE)/ar(ΔPFA) =ar(ΔQFD) /ar(ΔPFD)
III. ar(ΔPEA) =ar(ΔQFD)

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Answer 1

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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