Chapters

## Definition of a Polygon

**polygon**before, but what exactly is a polygon? In order to take a deep dive into what polygons are and what they are used for, let’s define what a polygon is. Take a look at the table below for a

**definition.**

Definition | |

Polygon | A polygon is a 2-dimensional shape that has 3 lines or more. Polygon is the main family for many different types of shapes. |

While we may not use the term polygon often to **describe** shapes in everyday life, the majority of the shapes we see everyday are polygons. Take a look at some examples below.

## Types of Polygons

In the previous section, we defined what a polygon was. This definition, however, is quite **broad** – and there’s a reason for it. You can think of the term polygon as a term used to describe a group of different **classifications** for shapes. Let’s take a look at some of those groups.

Polygons | |

Group 1 | Quadrilateral |

Group 2 | Parallelogram |

The two most common groups of shapes that are polygons are **quadrilaterals** and **parallelograms.** This might be getting confusing, so let’s simply start with what a polygon. Specifically, let’s take a look at what a polygon is not.

Take a look at the table below to see why it is **not** a polygon.

Circle | |

Two dimensional shape? | Yes |

Has three lines or more? | No |

## Quadrilaterals

Quadrilaterals are **“under”** the polygon definition. This means that all quadrilaterals are polygons, but not the other way around. This can be confusing, so let’s take a look at a **comparison.**

A | B |

All quadrilaterals are polygons but not all polygons are quadrilaterals | All dogs are animals but not all animals are dogs |

In order to understand what quadrilaterals are, let’s take a look at the **three** major properties that make a quadrilateral.

Property 1 | A two dimensional figure |

Property 2 | Made up of 4 line segments |

Property 3 | Opposite sides are congruent |

As you can see, the first two properties are the exact properties that define what polygons are. However, the if a polygon also has the **third property** listed above, it is a special type of polygon called a quadrilateral.

## Parallelogram

The other major type of polygon is called a parallelogram. Actually, a **parallelogram** is “under” the family of quadrilaterals. Similar to the way that quadrilaterals are a special **type** of polygon, parallelograms are a special type of quadrilateral.

Now, we have three levels of classifications for shapes.

Rule 1 | All quadrilaterals are polygons but not all polygons are quadrilaterals |

Rule 2 | All parallelograms are quadrilaterals but not all quadrilaterals are parallelograms |

You can think of these classifications as a **hierarchy.** Now, let’s take a look at the properties that all parallelograms have.

Property 1 | A two dimensional figure |

Property 2 | Made up of 4 line segments |

Property 3 | Opposite sides are congruent |

Property 4 | Opposite sides are parallel |

There are three **types** of parallelograms, all of which might be familiar to you. Take a look at them below.

## Common Polygons

Now that you’re familiar with polygons and the different classifications under the polygon **family,** let’s take a look at the most common types of polygons. The five **most common** polygons are listed in the table below.

1 | Triangle | Polygon |

2 | Rectangle | Parallelogram |

3 | Square | Parallelogram |

4 | Rhombus | Parallelogram |

5 | Trapezium | Quadrilateral |

Each shape is classified by its **“smallest”** classification. Meaning, a triangle is classified as a polygon at most, while a square goes all the way down the classification hierarchy to parallelogram.

## Naming Conventions

You may be wondering, how are polygons **named?** After all, we have seen some pretty odd names for types of polygons, such as parallelogram and quadrilateral. Let’s start with polygon itself. Take a look in the table below.

Poly | Polygon |

Many, much, one or more | Many sided shape |

The prefix poly- means many, which means that any shape that is a polygon has one or more sides. With some exceptions, such as the square, polygons are usually named by how **many sides** they have. Let’s take a look at some numbers and their corresponding prefixes.

Number | Prefix |

penta- | 5 |

hexa- | 6 |

hepta- | 7 |

octa- | 8 |

nona- | 9 |

deca- | 10 |

hendeca- | 11 |

dodeca- | 12 |

No matter what subject you’re in - biology, chemistry, maths - these prefixes apply to anything. In math **specifically,** to get the name of a shape, you simply need to know these prefixes and the number of sides the shape has.

## Polygons

As you saw in the previous section, all **numbers** have different prefixes. In order to get the name of a shape, you simply need to follow the rule in the table below.

Prefix | -gon | Example | Meaning |

Penta | -gon | Pentagon | 5 sided shape |

Now, let’s take a look at **different** polygons and see what they mean.

Polygon | Meaning |

Pentagon | 5 sided shape |

Hexagon | 6 sided shape |

Heptagon | 7 sided shape |

Octagon | 8 sided shape |

Nonagon | 9 sided shape |

Decagon | 10 sided shape |

Hendecagon | 11 sided shape |

Dodecagon | 12 sided shape |

Now that you know what each shape means, as well as what their name means, let’s take a look at what these **shapes** actually look like.

Image | Polygon |

A | Pentagon |

B | Hexagon |

C | Heptagon |

D | Octagon |

E | Nonagon |

F | Decagon |

G | Hendecagon |

H | Dodecagon |

As you can see, polygons are fairly easy to remember if you know what the **prefixes** in their names mean.

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