The answer is no the diagonals do not have to bisect each other. That does not necessarily mean that there isn't a quadrilateral that has bisecting diagonals. A quadrilateral is a four-sided polygon which is a close plane figure; in this case with four sides. Meaning that all ends of the straight lines that configure a polygon must connect someway, somehow.
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If you are talking about the diagonals of a quadrilateral, the only quadrilateral that have diagonals that are perpendicular and bisect each other is a square, because a rectangle has bisecting diagonals, while a rhombus has perpendicular diagonals. And a square fits in both of these categories.
diagonals.
the anser to this question is a trapiezuim as it could have right angles and its diagonals definatly do not bisect each other