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The most obvious types of quadrilaterals that have perpendicular diagonals are those with two pairs of adjacent sides the same length - squares, rhombuses, and "kite" shapes.

These are all special cases of "orthodiagonal" quadrilaterals. All orthodiagonal quadrilaterals will adhere to the rule that the sum of the squares of the lengths of two opposite (nonadjacent) sides will equal the sum of the squares of the lengths of the other two sides; for successive sides of lengths a, b, c, and d, we have:

a2 + c2 = b2 + d2

This formula will be true for all orthodiagonal quadrilaterals and any quadrilateral for which this is true will be orthodiagonal (i.e. the diagonals will be perpendicular).

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Q: Can you answer which quadrilaterals have their diagonals perpendicular?
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Related questions

Which quadrilaterals must have perpendicular diagonals?

A square, a rhombus and a kite are all 4 sided quadrilaterals that have perpendicular diagonals.

What are all of the quadrilaterals with perpendicular diagonals?

If a quadrilaterl has a perpendicular diagonas it is a roumbus, also kite has perperndicular diagonals

Are diagonals of a trapezoid perpendicular?

No, the only quadrilaterals that I can think of to have perpendicular diagonals are:KiteRhombusSquare (special case of a rhombus)

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Any type of rhombus has perpendicular diagonals. Please note that squares are a type of rhombus.

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rhombus, kite, square

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Squares, Rectangles, and Rhombuses.

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They are squares and rhombuses

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rhombus and a square

What quadrilaterals sides that are parallel to its opposite side and diagonals that are not perpendicular?

A parallelogram.

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They are 4 sided quadrilaterals such as a square, a rhombus and a kite.

What quadrilaterals Have diangles that are perpendicular to each other?

A square, a rhombus and a kite are three examples of quadrilaterals that have perpendicular diagonals that intersect each other at right angles.

Why does it make sense knowing the diagonals of a quadrilateral are perpendicular is not sufficient to show the quadrilateral is a rhombus?

It makes sense because it is true. There are other quadrilaterals whose diagonals are perpendicular.