Some of the most common geometric shapes are the triangle, the square, the pentagon, the octagon and the circle. All of these shapes, except the circle, are polygons, meaning they have a discrete number of sides and angles.
The word "polygon" is the most general name for a two-dimensional geometric shape composed of a discrete and finite number of line segments and angles. A polygon must be a closed figure and must lie in a two-dimensional plane. Each line segment composing a side of a polygon must intersect with only two other line segments. All exterior angles of a polygon must add up to a total of 360 degrees. The circle and ellipse, which are not composed of line segments and do not have any recognizable angles, constitute a second class of common geometric shapes. However, these shapes are not polygons.
Polygons can be either regular or irregular. Regular polygons are composed of a certain number of line segments, each equal in length, and the same number of angles, each equal in magnitude. Most common polygons, such as the equilateral triangle or the square, are regular polygons. A polygon is irregular if it fails to satisfy any of the conditions required of shapes that are considered regular polygons.