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# Concave and Convex Polygons

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 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.

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.