Library/Geometry/Plane geometry/Lines, rays, segments, and angles/Polygons

Polygons

Overview
Important

A polygon is a simple closed figure in the plane formed by a finite sequence of straight line segments (called sides) such that each segment meets exactly two others, one at each endpoint, and no two segments cross except at their endpoints.

Important properties

  • The number of sides (n) equals the number of vertices.

  • Polygons are classified by the number of sides: triangle (3), quadrilateral (4), pentagon (5), etc.

  • The sum of the interior angles of an n-sided polygon is (n-2) × 180°.

  • Polygons can be convex (all interior angles less than 180°) or concave (at least one interior angle greater than 180°).

  • A regular polygon has all sides and all angles equal.