One answer is a kite.
A square.
quadrilateral
A parallelogram.
Not all quadrilaterals with perpendicular diagonals are kites, but all kites have perpendicular diagonals. A kite is defined as a quadrilateral with two pairs of adjacent sides that are equal in length. While other quadrilaterals, such as certain types of rhombuses or irregular shapes, can also have perpendicular diagonals, they do not necessarily meet the criteria to be classified as kites.
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.
A square
A square.
How about a rectangle.
Sure, a square is a rectangle and the diagonals of a square are perpendicular.
False. Bisecting diagonals is sufficient to guarantee a parallelogram, but the diagonals will only be perpendicular if the sides of the parallelogram are equal.
trapezium
quadrilateral
A parallelogram.
A kite fits this description.
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.
The quadrilateral that must have diagonals that are congruent and perpendicular is the square. This is because its diagonals form a right angle at its center.
rhombus