State true or false:

If diagonals of a quadrilateral bisect each other, it must be a parallelogram.

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True

False

answer is A.

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Detailed Solution

Given a statement, if diagonals of a quadrilateral bisect each other, it must be a parallelogram.
We need to check if the given statement is true or false.
A parallelogram is a quadrilateral with its pair of opposite sides parallel and equal.
Also, its pair of opposite angles are equal and its diagonal bisect each other, as shown in the diagram below,
Question Image

So, we can conclude that if the diagonals of any quadrilateral are bisecting each other, then it must be a parallelogram.
Hence, the statement is true.
Hence, the correct option is (1).

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