Math, asked by sagar72427, 1 year ago

prove that the line segment joining the mid points of the opposite sides of a parallelogram divide it into four parallelograms of equal area

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Answered by sharmaaryanu6432432w
1

i hope it will help you to solve your problem

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Answered by Anonymous
0

Let us consider ABCD be a parallelogram in which E and F are mid-points of AB and CD. Join EF.

To prove: ar (|| AEFD) = ar (|| EBCF)

Let us construct DG ⊥ AG and let DG = h where, h is the altitude on side AB.

Proof:

ar (|| ABCD) = AB × h

ar (|| AEFD) = AE × h

= ½ AB × h ….. (1) [Since, E is the mid-point of AB]

ar (|| EBCF) = EF × h

= ½ AB × h …… (2) [Since, E is the mid-point of AB]

From (1) and (2)

ar (|| ABFD) = ar (|| EBCF)

Hence proved.

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