A 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 See more

The following animations show how to construct a square using a compass and straightedge. This is possible as 4 = 2 , a power of two See more

Every acute triangle has three inscribed squares (squares in its interior such that all four of a square's vertices lie on a side of the triangle, so two … See more

Squaring the circle, proposed by ancient geometers, is the problem of constructing a square with the same area as a given circle, by using only a finite number of steps with See more

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 See more

The coordinates for the vertices of a square with vertical and horizontal sides, centered at the origin and with side length 2 are (±1, ±1), while the interior of this square consists of all … See more

The square has Dih4 symmetry, order 8. There are 2 dihedral subgroups: Dih2, Dih1, and 3 cyclic subgroups: Z4, Z2, and Z1.
A square is a special case of many lower symmetry quadrilaterals:
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