Types of Polygons: Definition and Properties

Introduction

Geometric shapes can be defined as a figure or area closed by a boundary which is created by combining the specific number of curves, points, and lines.

The combination of the lines and curves forms different shapes. We got different names for the different types of figures. In this chapter, we will learn the names and properties of the figures.

The polygon with 4 sides is called a quadrilateral. The different types of polygons and their properties will be covered in this chapter.

Closed Figures

Figures in which initial and endpoints coincide with each other are called closed figures.

Closed Figure

Open Figures

Figures that have different initials and endpoints are called open figures.

Polygons:

In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape with straight sides. It does not have curved sides.

Here are a few examples of polygons.

Types of Polygons:

Depending on the sides and angles, the polygons are classified into different types, namely:

• Regular polygon
• Irregular polygon
• Convex polygon
• Concave polygon

Regular Polygon

If all the sides and interior angles of the polygon are equal, then it is known as a regular polygon. Examples of regular polygons are square, rhombus, equilateral triangle, etc.

Irregular Polygon

If all the sides and the interior angles of the polygon are of different measure, then it is known as an irregular polygon, for example, a scalene triangle, a rectangle, a kite, etc.

Convex Polygon

If all the interior angles of a polygon are strictly less than 180°, then it is known as a convex polygon. The vertex will point outwards from the center of the shape.

Concave Polygon

If one or more interior angles of a polygon are more than 180°, then it is known as a concave polygon. A concave polygon can have at least four sides, the vertex points towards the inside of the polygon.

Types of Polygons:

1. Line segments forming a polygon are called sides of the polygon.
2. The point where two sides of a polygon meet are called the vertex of the polygon.
3. The line segment containing two non-adjacent vertices is called the diagonal of the polygon.
4. The angles formed at the vertices inside the closed figure are called interior angles.

Note: The number of sides in a polygon is equal to the number of vertices.

Pentagon:

The five-sided polygon is called the pentagon polygon. When all five sides of the polygon are equal in length, then it is called a regular pentagon; otherwise, it is called an irregular pentagon.

Quadrilateral:

A quadrilateral polygon is also called a four-sided polygon or a quadrangle. The different types of quadrilateral polygons are square, rectangle, rhombus, and parallelogram.

Rhombus:

Let us go with an example of a rhombus, this is an equilateral polygon because it has equal sides, but it has unequal angles; therefore, it is an irregular polygon:

Irregular equilateral quadrilateral

Parallelogram:

A parallelogram is a special type of quadrilateral that has equal and parallel opposite sides.

The given figure shows a parallelogram ABCD in which AB is parallel to CD and AD is parallel to BC.

Also, AD = BC and AB = CD.

Octagon:

It is a polygon as it has eight sides.

Angles of an octagon: An octagon consists of eight angles. The sum of the angles of an octagon is 1080°.

• An octagon having eight congruent sides and angles is known as a regular octagon.
• Every regular octagon has the same angle measures.
• All sides are equal in length, and all the angles are equal in measure.
• The interior angles add up to 1080° (135×8), and the exterior angles add up to 360°.

Combination and Separation of Polygons:

1. Triangle 1 and triangle 2 can be combined to form a large triangle.
2. A large triangle can be subdivided into triangles 1 and triangle 2.

Example- Combination of Polygon:

You can combine two or more polygons into one polygon

Exercise:

1. Which of the following are polygons? Give reasons.

2. Which of the following are polygons? Circle them.

3. Draw the shapes of the following:

1. A triangle
2. A quadrilateral.

4. Name the kind of shapes given below

5. Guess the polygon

I am a plane figure with 4 sides of equal lengths and 90-degree angles on the sides.

I am a plane figure with 2 sides, each of equal length and 90-degree angles on the
sides.

I am a plane figure with 6 sides, and all interior angles are greater than 90 degrees.

6. Match the following:

	Column-A		Column-B
(a)	Pentagon	(i)	8-sided polygon
(b)	Hexagon	(ii)	3-side polygon
(c)	Quadrilateral	(iii)	5-side polygon
(d)	Triangle	(iv)	6-side polygon
(e)	Octagon	(v)	4-side polygon

Match the Column A with B

7. What is the sum of the interior angles of a quadrilateral?

8. An irregular octagon has one interior angle of 130°. What is the size of the adjacent exterior angle?

9. The three angles of a quadrilateral are 76°, 54°, and 108°. Find the measure fourth angle.

10. Draw a pair of parallel lines.