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Chapter 3: Polygons and Their Relations

# The Basics

Before you dive into the relationships between polygons, you should have basic knowledge of polygons. Polygons commonly include triangles, squares/rectangles, and circles. They are closed figures and have at least three sides. They have length and width but no thickness. Although there are infinite types of polygons, we are going to just deal with triangles, squares/rectangles, rhombus, and trapezoids. Followings are some other basic concepts of polygons:

A diagonal of a polygon is a segment joining two nonconsecutive vertices.

A polygon is convex if the segment joining any two interior points of the polygon is in the interior of the polygon. If a polygon is not convex, then it is concave.

A regular polygon is a convex polygon that is both equilateral and equiangular.

All polygons have interior angles and exterior angles. Following are some properties of interior and exterior angles of polygons:

The sum of the measures of the interior angles of a convex polygon with n sides is (n-2)180.

The sum of the measures of the interior angles of a convex quadrilateral is 360.

The measure of an angle of a regular polygon with n sides is (n-2)180/n.

The sum of the measures of the exterior angles, one at each vertex, of any convex polygon is 360.

The measure of an exterior angle of a regular polygon with n sides is 360/n.

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