perpendicular
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rhombus, kite, square
Square, rhombus or a kite.
perpendicular. meaning that they make a right angle when they cross
From Wikipedia: '...a kite, or deltoid, is a quadrilateral with two disjoint pairs of congruent adjacent sides, in contrast to a parallelogram, where the congruent sides are opposite.' In other words, a kite consists of two isosceles triangles joined at the base. Beginning with a particular isosceles triangle, it will always be possible to construct from it one kite that has equal diagonals (given that the kite may be either convex or concave). Hence an infinite number of kites do have equal diagonals, but many do not. A notable example of a kite that does have equal diagonals is a square.
The area of a quadrilateral kite is 0.5 times the product of its diagonals.