Characterizations
A convex quadrilateral is a square if and only if it is any one of the following:
- a rectangle with two adjacent equal sides
- a quadrilateral with four equal sides and four right angles
- a parallelogram with one right angle and two adjacent equal sides
- a rhombus with a right angle
- a rhombus with all angles equal
- a quadrilateral where the diagonals are equal and are the perpendicular bisectors of each other, i.e. a rhombus with equal diagonals
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