If sides AB and CD of a parallelogram ABCD are bisected at E and F then EBFD is a parallelogram.

True

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False

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Solution

The correct option is A True
Based on the given statement, we can draw the figure shown above.

Here, $A B C D$ is a parallelogram
$∴ E B = \frac{1}{2} A B = \frac{1}{2} D C = D F$

and $E B ∥ D F$ $(∵ A B ∥ D C)$

Thus, one pair of opposite sides of the quadrilateral $E B F D$ is equal and parallel.
Hence, $E B F D$ is a parallelogram.

Therefore, the given statement is true.

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