Any regular polygon with 4n sides, where n is a positive integer.
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Rectangle
The diagonals of an isosceles trapezoid are equal in lengths but are not perpendicular to each other at right angles.
square
It could be a square, but consider the following congruent & perpendicular 'diagonals of a quadrilateral (you will have to connect the endpoints of the diagonals, yourself, as it cannot be drawn in text): . _|___ . | . | . | If the two diagonals, also bisect each other, then it's a square, otherwise it is not.
Yes, the diagonals of a square are congruent (equal in length) and are perpendicular.