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In the given figure, ABCD is a parallelogram in which $ E $ and $ F $ are points on $ A B $ and CD respectively, such that $ B E=\frac{1}{2} A B $ and $ D F=\frac{1}{2} D C $. Prove that BEDF is a parallelogram.
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Given:

ABCD is a parallelogram.

\( B E=\frac{1}{2} A B \) and \( D F=\frac{1}{2} D C \).

To do:

We have to prove that BEDF is a parallelogram.
Solution:

$AE=BE=\frac{1}{2}AB$

$CF=DF=\frac{1}{2}CD$
Therefore,

$BE=DF$   (Since $AB=CD$, opposite sides of a parallelogram are equal)
$BE\parallel DF$ 

This implies,

BEDF is a parallelogram.

Hence Proved.

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Updated on: 10-Oct-2022

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