What is a Polygon?

A polygon is a closed shape with straight sides. The sides of a polygon are line segments, and the place where two sides meet is called a vertex. Polygons are named by the number of sides they have. For example, a polygon with three sides is called a triangle, a polygon with four sides is called a quadrilateral, and so on.

Types of Polygons

There are several types of polygons based on the number of sides they have:

Triangle: A polygon with three sides.
Quadrilateral: A polygon with four sides.
Pentagon: A polygon with five sides.
Hexagon: A polygon with six sides.
Heptagon (or Septagon): A polygon with seven sides.
Octagon: A polygon with eight sides.
Nonagon (or Enneagon): A polygon with nine sides.
Decagon: A polygon with ten sides.

Properties of Polygons

Here are some important properties of polygons:

Interior Angles: The sum of the interior angles of a polygon with n sides is given by the formula: (n - 2) * 180 degrees.
Exterior Angles: The sum of the exterior angles of any polygon is always 360 degrees.
Diagonals: A diagonal is a line segment that connects two non-adjacent vertices of a polygon. The number of diagonals in a polygon can be calculated using the formula: n(n-3)/2, where n is the number of sides.

Study Guide

When studying polygons, it's important to:

Memorize the names and properties of common polygons, including triangles, quadrilaterals, pentagons, hexagons, and octagons.
Understand the formulas for calculating interior and exterior angles, as well as the number of diagonals in a polygon.
Practice identifying and drawing different types of polygons.
Solve problems involving the properties of polygons, such as finding missing angles or sides.