A kite, a square or a rhombus
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That is a parallelogram.
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 + d2This 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).
A rhombus has four sides that are all the same length ---------------------------------------- but if you are talking about the geometric shape kite - it is not a rhombus. A kite has two adjacent sides of equal length and the other two sides of equal length. Only a square can be a rhombus.
parallelogram * * * * * Not true. Rectangles and squares do, but other parallelograms do not.
Quadrilaterals are called parallelograms ONLY if both pairs of opposite sides are equal and parallel to each other.