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The sides A B\ a n d\ C D of a parallelo...

The sides `A B\ a n d\ C D` of a parallelogram `A B C D` are bisected at `E\ a n d\ Fdot` Prove that `E B F D` is a parallelogram.

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`A B C D`is a parallelogram
`BE=1/2AB and DF=1/2 CD`(E and F is mid point of AB and CD)
`AB|| CD \and\ AB=CD`(opposite sides of parallelogram is are parallel and equal)
`1/2 AB=1/2CD \and\ 1/2 AB=1/2 CD`
`BE||DF \and\ BE=DF`
So In `square E B F D` one pair of opposite side is parallel and equal.
`E B F D` is a parallelogram.
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