So you think you know your squares and rectangles? If so, then you probably already know what quadrilaterals, parallelograms and quadrangles are, but if not, then you might want to know more about these two polygons.

## Definitions

**Square** – In geometry, a square is a four-sided polygon called a quadrilateral. Aside from being called a quadrilateral, it is also labeled as a *parallelogram* (opposite sides are parallel to each other). But there are many four-sided polygons such as trapezoids, cyclic quadrilaterals, trapeziums etc., so what makes a square different from the others? It is actually a regular quadrilateral, and according to *Euclidean geometry* (a mathematical system attributed to the Alexandrian Greek mathematician Euclid), it means a square is a polygon that is *equiangular* (all angles are equal in measure) and *equilateral* (all sides are equal in length).

### Properties of a Square

- All four angles are equal at 90°
- All four sides are equal in length
- Opposite sides are parallel
- The diagonals
*bisect*(divided into two equal parts) its angles - The diagonals
*bisect*each other and meet at 90° - The diagonals are equal in length

*Note:* A square can also be defined as a special *rectangle,* since the opposite sides of a square are parallel to each other, and is also a special case of a *rhombus* (having four equal sides).

**Rectangle** – In Euclidean geometry, a rectangle is also a quadrilateral and as with the square, has four equal angles at 90°. It can also be labeled as a parallelogram since its opposite sides are parallel to each other.

### Properties of a Rectangle

- All four angles are equal at 90°
- Opposite sides are equal in length
- Opposite sides are parallel
- The diagonals are equal in length

## Comparison

While it may be a little bit confusing since a square is also a rectangle, there is one difference that makes it easy to distinguish one from the other.

Both a square and a rectangle may have their four angles at 90°, have parallel opposite sides with the same length, and have their diagonals equal in length, but only a square has four sides of equal length. Take note however, a square is also considered a special case of a rectangle, which means a square isn’t primarily a rectangle, but more an example of a rectangle.

To summarize, a square is somewhat a rectangle since it does have all the properties of being a rectangle, but it needs to have its sides equal in measurement to be called a square.

## Comparison Chart

Square | Rectangle |

It is a quadrilateral | It is a quadrilateral |

It is a parallelogram | It is a parallelogram |

All angles are equal at 90° | All angles are equal at 90° |

Diagonals are equal in length | Diagonals are equal in length |

Opposite sides are parallel | Opposite sides are parallel |

All sides are equal | Opposite sides are equal |

## Video

Here is a video that talks about the properties of both square and rectangle.