square - choose a jigsaw puzzle to solve

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted ◻ {\displaystyle \square } ABCD. 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 rhombus with a right vertex angle a rhombus with all angles equal a parallelogram with one right vertex angle and two adjacent equal sides a quadrilateral with four equal sides and four right angles a quadrilateral where the diagonals are equal and are the perpendicular bisectors of each other, i.e. a rhombus with equal diagonals a convex quadrilateral with successive sides a, b, c, d whose area is A = 1 2 ( a 2 + c 2 ) = 1 2 ( b 2 + d 2 ) . {\displaystyle A={\tfrac {1}{2}}(a^{2}+c^{2})={\tfrac {1}{2}}(b^{2}+d^{2}).} A square is a special case of a rhombus (equal sides, opposite equal angles), a kite (two pairs of adjacent equal sides), a trapezoid (one pair of opposite sides parallel), a parallelogram (all opposite sides parallel), a quadrilateral or tetragon (four-sided polygon), and a rectangle (opposite sides equal, right-angles) and therefore has all the properties of all these shapes, namely: The diagonals of a square bisect each other and meet at 90° The diagonals of a square bisect its angles. Opposite sides of a square are both parallel and equal in length. All four angles of a square are equal. (Each is 360°/4 = 90°, so every angle of a square is a right angle.) All four sides of a square are equal. The diagonals of a square are equal. The square is the n=2 case of the families of n-hypercubes and n-orthoplexes.