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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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Which two quadrilaterals have perpendicular diagonals?
Any type of rhombus has perpendicular diagonals. Please note that squares are a type of rhombus.
What quadrilaterals have parallel sides and perpendicular diagonals?
They are squares and rhombuses
What quadrilaterals have diagonals perpendicular to each other?
rhombus and a square
What quadrilaterals sides that are parallel to its opposite side and diagonals that are not perpendicular?
A parallelogram.
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.
