No, not unless it is also a square.
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No the diagonals of a rectangle are not perpendicular because they do not cross each other at right angles
Rectangle
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.
Not always because the diagonals of a rectangle bisect each other but they are not perpendicular to each other.
A rectangle