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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