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Question

Two parallelograms ABCD and EFCD that have the same base CD and lie on the same parallels AF and CD, then

A
Area(ABCD) = Area(AFCD)
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B
Area(ABCD) = Area(EFCD)
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C
Area(EBDC) = Area(EFCD)
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D
None of these
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Solution

The correct option is B Area(ABCD) = Area(EFCD)
ABCD is a parallelogram, then ADBC
& AB is transversal , therefore
DAB=CBF(1) (corresponding angles)
Also AD=BC(2) (opposite sides of gm)
Similarly in gm CDEF,
EDCF & EF is transversal , therefore
DEA=CFE(3)
(corresponding angles)
In AED & BFC
DEA=CFE [from(3)]
AD=BC [from(2)]
DAB=CBF [from (1)]
AEDBFC (By ASA congruency)
arAED=arBFC (areas of congruent part)
Now, arABCD=arADE+arEBCD
=arBFC+arEBCD
arABCD=arEFCD

969511_1054862_ans_f0cdea6d53c841e58b08e80f4f9dae88.png

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