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One answer is a kite.
If the diagonals of a quadrilateral are perpendicular to each other, then the quadrilateral is a square.Or a kite.
It can be but a square and a rhombus diagonals are also perpendicular and therefore intersect at 90 degrees and they too are both quadrilaterals.
A square, a rhombus and a kite have diagonals that intersect each other at right angles.
It is a kite.