# Concave and Convex Polygons

Rate Lesson0 stars
Lesson size:
Message preview:
Someone you know has shared lesson with you:

To play this lesson, click on the link below:

https://www.turtlediary.com/lesson/concave-and-convex-polygons.html

Hope you have a good experience with this site and recommend to your friends too.

Login to rate activities and track progress.
Login to rate activities and track progress.

## Convex Polygons

A convex polygon is a polygon in which every angle is less than 180o.

## Concave Polygons

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

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 180o.

### Example 2

Is this polygon concave or convex?

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

### Example 3

Is this polygon concave or convex?

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

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 do not lie inside the polygon, then it is a concave polygon.

Summary
• A convex polygon is a polygon in which every angle is less than 180o.
• A concave polygon is a polygon in which at least one angle is more than 180o.
• 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.
This lesson has been watched 6,634 times.

I'm looking for