A convex quadrilateral is a square in special conditions as follows:
- A rectangle with two adjacent equal sides.
- A rhombus with a right angle, all angles equal, equal diagonals.
- A parallelogram with one right angle and two adjacent equal sides makes a square.
- An isosceles trapezoid with equal diagonals, base angle equals.
- A Kite with two disjoint pairs of adjacent sides is equal.