# Geometric shapes: Types and properties

## In a nutshell

Geometric shapes are structures made up of lines, curves and points. Geometric shapes, such as triangles and quadrilaterals, can be classified according to their properties.

## Regular and irregular shapes

Shapes are regular if their sides are the same length. Irregular shapes have sides of different lengths. Below on the left is a regular pentagon. Below on the right is an irregular pentagon.

**Note: ***All the interior angles of regular shapes are equal.*

## Triangles

There are four types of triangle:

- Equilateral - three equal sides and three equal angles (all 60$\degree$).

- Isosceles - two equal sides and two equal angles.
- Scalene - no equal sides and all angles different.
- Right-angled - one angle is a right angle (90$\degree$).

**Note:**** **In diagrams of shapes, lines of equal length are sometimes marked with dashes, and parallel lines are marked with arrows.

## Quadrilaterals

Quadrilaterals are four-sided shapes. There are a number of variations, some of which are shown in the table below:

#### SHape name | #### properties | #### diagram |

Square | - All angles are 90$\degree$.
- All sides are equal in length.
- Opposite side are parallel.
| |

Rectangle | - All angles are 90$\degree$.
- Opposite sides are equal in length.
- Opposite sides are parallel.
| |

Parallelogram | - Diagonally opposite angles are equal.
- Opposite sides are equal in length.
- Opposite sides are parallel.
| |

Rhombus | - Diagonally opposite angles are equal.
- All sides are equal in length.
- Opposite sides are parallel.
| |

Trapezium | - One pair of opposite sides is parallel.
| |

**Tip: ***A rhombus can be thought of as a squashed square, and a parallelogram as a squashed rectangle.*