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

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