Теория:

A convex quadrilateral is a square in special conditions as follows:
 
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  • rectangle with two adjacent equal sides.
  • A rhombus with a right angle, all angles equal, equal diagonals.
  • 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.