# Concave and Convex Polygons

## Convex Polygons

A convex polygon is a polygon in which **every angle is less than 180 ^{o}**.

## Concave Polygons

A concave polygon is a polygon in which **at least one angle is more than 180 ^{o}**.

Let's go through some examples.

**Example 1**

**Is this polygon concave or convex?**

This is a concave polygon as two of its angles are more than 180^{o}.

**Example 2**

**Is this polygon concave or convex?**

This is a concave polygon as one of its angles is more than 180^{o}.

**Example 3**

**Is this polygon concave or convex?**

This is a convex polygon as all its angles are less than 180^{o}.

**Note:**

We know that a **diagonal** is a line segment connecting two non-consecutive vertices of a polygon.

For example:

This polygon has 5 diagonals.

Notice that polygons that are convex have no portions of their diagonals in their exteriors.

So, we can say that:

**If all the diagonals of a polygon lie inside the polygon, then it is a convex polygon.**

**If all the diagonals of a polygon do not lie inside the polygon, then it is a concave polygon.**

- A convex polygon is a polygon in which every angle is less than 180
^{o}. - A concave polygon is a polygon in which at least one angle is more than 180
^{o}. - A diagonal is a line segment connecting two non-consecutive vertices of a polygon.
- If all the diagonals of a polygon lie inside the polygon, then it is a convex polygon.
- If all the diagonals of a polygon do not lie inside the polygon, then it is a concave polygon.