Square - Characterizations

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