Polygons

A polygon is a closed figure formed by three or more line segments. The line segments are called the sides of the polygon. The point where two sides meet is called a vertex.

Types of Polygons

There are many types of polygons, some of the common ones include:

• 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: A polygon with nine sides.
• Decagon: A polygon with ten sides.

Properties of Polygons

There are several important properties of polygons:

1. Number of Sides: The number of sides determines the type of polygon.
2. Interior Angles: The sum of the interior angles of a polygon with n sides is given by the formula: (n-2) * 180 degrees.
3. Exterior Angles: The exterior angle of a polygon is the angle formed between one side of the polygon and the extension of an adjacent side. The sum of the exterior angles of any polygon is always 360 degrees.
4. Regular and Irregular Polygons: A polygon is called regular if all its sides and angles are equal. If any of the sides or angles are different, it is called irregular.

Study Guide

When studying polygons, it's important to understand the following concepts:

1. Identifying and naming different types of polygons based on their number of sides.
2. Calculating the sum of interior angles in a polygon using the formula (n-2) * 180 degrees.
3. Finding the measure of each interior angle in a regular polygon.
4. Understanding the concept of regular and irregular polygons.
5. Applying the properties of polygons to solve problems and calculate missing angles or side lengths.

By mastering these concepts, you will have a solid understanding of polygons and be able to solve various problems related to them.