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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)`.

Text Solution

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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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