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# Polygons 2

**Quadrilaterals** are 4-sided shapes and are probably the most interesting of all the polygons as there are several ones with special properties and names.

**Square:**

- All sides equal.
- All angles 90
^{0}. - 4 lines of symmetry.
- Rotation symmetry of order 4.

**Rectangle:**

- Two pairs of equal and parallel sides.
- All angles 90
^{0}. - Two lines of symmetry.
- Rotation symmetry of order 2.

**Rhombus:**

- All sides equal.
- Opposite sides parallel.
- Two lines of symmetry.
- Rotation symmetry of order 2.
- Basically, a square leaning over. Sometimes referred to as a diamond!

**Parallelogram:**

- Two pairs of equal and parallel sides.
- Opposite angles equal.
- No lines of symmetry.
- Rotation symmetry of order 2.
- Basically, a rectangle leaning over.

**Trapezium:**

- One pair of parallel sides.
- No symmetry.

**Kite:**

- Two pairs of equal sides next to each other.
- One line of symmetry.
- No rotation symmetry.

There are two types of angle when dealing with Polygons - **internal** and **external.**

You need to be able to work them out for **regular polygons **(that's polygons which have all sides equal and all angles equal).

The easiest thing to do is work out the **external** angle. The internal angle is then just the difference between that and 180^{0}.

The external angle is the angle that you must turn for each new side. When you have drawn the whole shape you will be back where you started so you must have travelled 360^{0}. Therefore, the external angle is simply 360^{0} divided by the number of sides (or the number of "turns").

**For a regular polygon with 'n' sides, External angle:**

So to work out the internal angle we just subtract that from 180^{0}.

**For a regular polygon with 'n' sides, Internal angle:**

**For example:**

For a pentagon...

Here's a useful table with them all in:

Polygon: |
Number of sides: |
External angles: |
Internal angles: |

Triangle |
3 | 120 | 60 |

Square |
4 | 90 | 90 |

Pentagon |
5 | 72 | 108 |

Hexagon |
6 | 60 | 120 |

Heptagon |
7 | 51.4 | 128.6 |

Octagon |
8 | 45 | 135 |

Nonagon |
9 | 40 | 140 |

Decagon |
10 | 36 | 144 |

Undecagon |
11 | 32.7 | 147.3 |

Dodecagon |
12 | 30 | 150 |