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# In the given figure, ABCD is a parallelogram. If E AND F are midpoints of BC and AD respectively, then which of the following statements is correct?

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Solution

## ABCD is a parallelogram ....(given) E is the midpoint of BC and F is the midpoint of AD ..... (given) Therefore, BE = EC = AF = FD BEFA and ECDA are parallelograms .... Therefore, area of //gm ACEF = area of //gm ECDF ..... (i) (parallelograms having equal bases and between the same parallels are equal in area) Area Δ DEF=12 area //gm ECDF ..... (area of triangle is half the area of parallelogram if they have the same base and between the same parallels) Area Δ DEF=12 area //gm AFEB ..... (from(i)).... (ii) Area Δ ABE=12 area //gm AFEB ..... (area of triangle is half the area of parallelogram if they have the same base and between the same parallels) Therefore Area Δ ABE = Area Δ DEF ..... (from(ii)) Area Δ AED12 area //gm ABCD ….(area of triangle is half the area of parallelogram if they have the same base and between the same parallels)  Suggest Corrections  0      Similar questions
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