CBSE Class 9 Answered
Expert Answer
Given : To ||gm ABCD and EFCD are on the same base DC and between the same parallels AF and DC
To prove: ar(||gm ABCD) = ar(||gm EFCD)
Proof
: In 
ADE and BCF
DAE
= CBF
AED
= BFC
[Corresponding 's]
ADE = BCF (Angle sum property of a triangle)
AD = BC (opposite sides of the ||gm)
ar(ADE) = ar(BCF) (Congruent figure have equal areas)
Now, ar(ABCD) = ar(ADE) + ar(EDCB)
= ar(BCF) + ar(EDCB)
= ar(EFCD)
So, ||gm ABCD and ||gm EFCD are equal in area.
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ADF = area of 
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