Polygon
A polygon is a closed plane figure formed by three or more line segments. The following are a few examples.
The line segments that form a polygon are called sides. Two connected sides form an angle at a point called a vertex. A diagonal is a line segment joining two non-consecutive vertices. In the polygon below, , , , and are four sides. They form four angles: ∠A, ∠B, ∠C, and ∠D. and are two diagonals.
There are many ways to classify polygons; the following are some of them.
Regular and irregular polygons
Regular polygon
A regular polygon is a polygon in which all sides have equal length (equilateral) and all angles have equal measure (equiangular). Below are some examples.
Irregular polygon
An irregular polygon has sides or angles that are not congruent, as shown below.
Convex and concave polygons
Polygons can be classified as either convex or concave.
Convex polygon
If all the interior angles of a polygon are less than 180°, it is convex. A regular polygon is always convex. The following are a few examples.
Concave polygon
If one or more interior angles of a polygon are larger than 180°, it is concave. A concave polygon is always an irregular polygon. The following are a few examples. The interior angles larger than 180° are marked with a red arc.
Classifying polygons by their number of sides
Polygons are commonly classified based on the number of sides they have. In general, a polygon with n-number of sides is called an n-gon. Some important polygons have specific names, such as triangles, pentagons, hexagons, etc. The following are some examples.
| Polygon | # of sides | Shape |
|---|---|---|
| Triangle | 3 |  |
| Quadrilateral | 4 |  |
| Pentagon | 5 |  |
| Hexagon | 6 |  |
| Octagon | 8 |  |
There are many other polygons, and each polygon above can be further classified. For example, a triangle can be further classified as an acute, obtuse, or right triangle. Learn more about these polygons by navigating this website.