A polygon is a two dimensional shape formed by connecting three or more line segments at vertices. The term originates from the Greek word "poly" which means "many" and "gon" which means "a closed figure".

A polygon with three sides is a called a triangle. A polygon with four sides is called a quadrilateral. Special cases of quadrilaterals include shapes like trapezoids, rectangle, rhombuses and squares. A polygon with five sides is a called a pentagon. A polygon with six sides is a called a hexagon. A polygon with eight sides is a called an octagon.

Angle Rules for Polygons

  • In any triangle, the sum of the three angles is 180 degrees.
  • In any quadrilateral, the sum of the four angles is 360 degrees.

The sum of interior angles of n sided polygon = (n - 2) × 180 degrees

Regular Polygons

For a polygon to be regular, it must satisfy both of the following conditions:

  1. The polygon must be equilateral: All sides must have the same length
  2. The polygon must be equiangular: All angles must have the same measure