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The sides A B and C D of a parallelogram...

The sides `A B` and `C D` of a parallelogram `A B C D` are bisected at `Ea n dF` . Prove that `E B F D` is a parallelogram.

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Given: In parallelogram ABCD, E and F are the midpoints of the side AB and CD respectively.
DE and BF are joined.
To prove : EBFD is a parallelogram.
Construction: Join EF.
Proof :
∵ABCD is a parallelogram
∴AB = CD and AB || CD
(Opposite sides of a parallelogram are equal and parallel)
∴ EB || DF and EB = DF
(∵ E and F are mid points of AB and CD)
∴ EBFD is a parallelogram.
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