Polygons

A polygon is a closed shape with straight sides. The sides of a polygon are line segments and the points where the sides meet are called vertices. The number of sides and vertices in a polygon can vary, depending on the shape. Polygons are named based on the number of sides they have. Here are some common polygons:

Triangle: A polygon with three sides and three vertices.
Quadrilateral: A polygon with four sides and four vertices.
Pentagon: A polygon with five sides and five vertices.
Hexagon: A polygon with six sides and six vertices.
Heptagon: A polygon with seven sides and seven vertices.
Octagon: A polygon with eight sides and eight vertices.
Nonagon: A polygon with nine sides and nine vertices.
Decagon: A polygon with ten sides and ten vertices.

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 joins 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.

Types of Polygons

Polygons can be classified into different types based on the number of sides and angles. Here are some common types of polygons:

Regular Polygon: A polygon with all sides and angles equal is called a regular polygon.
Irregular Polygon: A polygon with sides and/or angles that are not all equal is called an irregular polygon.
Convex Polygon: A polygon in which all interior angles are less than 180 degrees is called a convex polygon.
Concave Polygon: A polygon in which at least one interior angle is greater than 180 degrees is called a concave polygon.

Study Guide

Here are some key points to remember when studying polygons:

Understand the definition of a polygon and be able to identify different types of polygons based on the number of sides and vertices.
Memorize the formulas for calculating the sum of interior angles and the number of diagonals in a polygon.
Be familiar with the properties of regular, irregular, convex, and concave polygons.
Practice identifying and drawing different types of polygons to reinforce your understanding.
Work on solving problems and exercises related to polygons to improve your skills in this topic.

Understanding polygons is important as they are fundamental shapes in geometry and have many real-world applications. Make sure to review the material thoroughly and practice regularly to master this topic.