In elementary geometry, a polygon is a plane figure that is bounded by a finite chain of straight line segments closing in a loop to form a closed chain or circuit. Or simply a closed plane figure bounded by three or more line segment to form a closed loop is called a polygon.
- The line segments forming the polygon are called sides.
- The point of intersection of two line segments is called a vertex.
- Number of vertices of a polygon is equal to the number of line segments or sides.
Different types of Polygons: This is based on the number of sides that the polygon has. Here are few examples:
Diagonal of a Polygon: A line segment joining any two non-consecutive vertices is called
a diagonal of the polygon.
The dotted lines are diagonals of the shown polygons.
Interior and Exterior Angles of a Polygon: This is an important concept.
are interior angles. These are made by the two sides of the polygon.
is called an exterior angle. This is formed by extending a side of the polygon as shown in the adjacent figure.
Just by looking at the figure you can tell that
Hence we can say that:
Exterior Angle + Adjacent Interior Angle
Convex Polygon vs Concave Polygon
If the interior angle of the polygon is less than , then it is called convex polygon. If you look at any of the polygons shown above, you will see that all the interior angles are less than .
But there can be cases where the interior angle of a polygon could be more than . Take a look at the adjacent figure. Here you will see that (which is a reflex angle).
Regular Polygon: A polygon that satisfies the following condition is called a regular polygon.
- All sides are equal
- All interior angles are equal
- All exterior angles are equal
For a regular polygon with sides we have the following:
A polygon can be divided into triangles.
See a few examples in the adjacent figure.
We know that the sum of the angles of a triangle is .
From the above point 2, we can also say that
We already know that