# Square

A square is a quadrilateral with four right angles and four congruent sides, as shown in the figure below. A square is a regular quadrilateral.

In algebra, the square of a number is the number multiplied by itself. For example, the square of n is written as "n^{2}" and is equal to n × n.

## Sides of a square

The sides of a square are congruent. Also, the opposite sides of a square are parallel, and the adjacent sides are perpendicular to each other.

In the square below, AB//CD and AD//BC. Also, AD and BC are perpendicular to AB and CD respectively.

## Angles of a square

The angles of a square are all congruent and equal to 90°. Accordingly, the external angles of a square are also right angles. In the diagram above, the angles marked with a red square are all right triangles.

## Diagonals of a square

A square has two congruent diagonals. The diagonals of a square have special properties:

- The two diagonals perpendicular bisectors of each other. The point of intersection of the diagonals is the center of the square (E in the figure below). and in the figure below of a square are
- The diagonals of a square bisect its angles, forming 8 congruent angles, each measuring 45°, forming two pairs of four congruent 45°-45°-90° triangles: △ABC, △ADC, △BAD, and △BCD; △ABE, △ADE, △BCE, and △CDE.

## Special quadrilaterals

A square is a regular quadrilateral. It is also a special case of a parallelogram, rectangle, rhombus, trapezoid, and kite:

## Symmetry in a square

As a regular quadrilateral, a square has 4 lines of symmetry and a rotational symmetry of order 4, which means that it can be rotated in such a way that it will look the same as the original shape 4 times in 360°.

Line of symmetry | Rotational symmetry |
---|---|

4 lines of symmetry | Four 90° angles of rotation |

## Area and perimeter of a square

Given that a square has four right angles and four congruent sides, the area and perimeter of a square are:

area = a^{2}

perimeter = 4a

where a is the length of the side.