Polygons (Jump to: Lecture | Video )

Polygon
A polygon is a closed figure made up of 3 or more line segments.

Figure 1.

Above are a few examples of figures that are polygons.

A figure is not a polygon if:

It is an open figure.

Figure 2.

The sides of the figure overlap.

Figure 3.

It has a side that is not a line segment.

Figure 4.

Polygons can be named by the number of sides they have. Here are some examples:

Figure 5.

Interior Angles
The interior angles of a polygon sum to (n – 2)180 degrees, where n is the number of sides.

Figure 6.

The above figure has 6 sides, so:

(6 - 2)180 = (4)180 = 720

It has 720 degrees.

Exterior Angles
For any polygon, all exterior angles sum to 360 degrees.

Figure 7.

All of the green angles of this polygon sum to 360 degrees.

Regular Polygons
A regular polygon is a polygon where every side is equal to one another, and every angle is equal to one another.

Below are two examples of regular polygons:

Figure 8.

---