# Polygon

What is a Polygon?

A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments.

Now, observe the following simple closed curves:

Curves 1, 3 and 4 are made of line segments only, while curves 2 and 5 are made of line segments and curves.

Curves 1, 3 and 4 are called polygons.

A simple closed curve made of line segments only is called a polygon.

All the following figures are polygons.

The line-segments of a polygon are named by the sides in it. Poly means many and gon means sides. Thus a polygon has many sides.

Definition of Polygons: Simple closed figures having three or more line segments are called polygons.

Polygons are further divided into various categories, depending upon the line segments they have.

The different polygons having definite number of sides are given names according to the number of sides.

(i) A polygon with three sides is called a triangle.

or,

A polygon having three line segments is called a triangle.

The three line segments forming the triangle are its sides.

Triangle

(ii) A polygon with four sides is called a quadrilateral.

or,

A polygon having four line segments is called a quadrilateral.

(iii) A square is a quadrilateral whose all the four sides are equal.

(iv) A rectangle is a quadrilateral whose opposite sides are equal.

(v) A polygon with five sides is called a pentagon.

Pentagon

(vi) A polygon with six sides is called a hexagon.

Hexagon

Thus a polygon is given its name on the basis of the number of its sides.

Sides, Vertices and Diagonals of a Polygon:

Sides: The line segments forming a polygon are called its sides.

In the above figure, the sides of the polygon ABCDE are AB, BC, CD, DE, ΕΑ.

Vertices: The meeting point of a pair of sides is called a vertex.

In the above figure, sides AE and ED meet at E. So E is a vertex of the polygon ABCDE. A, B, C and D are its other vertices.

Adjacent Sides: Any two sides with a common end point are called the adjacent sides of the polygon.

In the above polygon ABCDE, (AB, BC), (BC, CD), (CD, DE), (DE, EA) and (EA, AB) are the adjacent sides.

Adjacent Vertices: The end points of the same side of a polygon are called adjacent vertices.

In the above polygon ABCDE, vertices E and D are adjacent, whereas A and D are not adjacent vertices. Other adjacent vertices in the figure are (A, B), (B, C), (C, D) and (E, A).

Diagonals: The joins of the pairs of vertices which are not adjacent, are called diagonals of the polygon.

In the above polygon ABCDE, AC, AD, BD, BE and CE are diagonals.

Worksheet on Polygons:

1. Tick the polygons which are quadrilaterals:

2. Fill in the blanks:

(i) All the sides of a __________ are equal.

(ii) A polygon made of four line segments is called a __________ .

(iii) A polygon made of three line segments is called a __________ .

(iv) A simple closed curve made of line segments only is called a __________ .

(v) A closed curve which does not cross itself is called a __________ curve.

## You might like these

• ### Simple Closed Curves | Types of Closed Curves | Collection of Curves

In simple closed curves the shapes are closed by line-segments or by a curved line. Triangle, quadrilateral, circle, etc., are examples of closed curves.

• ### What is a Triangle? | Types of Triangle | Scalene Triangle | Isosceles

A simple closed curve or a polygon formed by three line-segments (sides) is called a triangle. The above shown shapes are triangles. The symbol of a triangle is ∆. A triangle is a polygon with three sides. In the given figure ABC is a triangle. AB, BC and CA are its sides.

• ### Circle Math | Terms Related to the Circle | Symbol of Circle O | Math

In circle math the terms related to the circle are discussed here. A circle is such a closed curve whose every point is equidistant from a fixed point called its centre. The symbol of circle is O. We have learned to draw a circle, by tracing the outlines of objects like a

• ### Symmetrical Shapes | One, Two, Three, Four & Many-line Symmetry

Symmetrical shapes are discussed here in this topic. Any object or shape which can be cut in two equal halves in such a way that both the parts are exactly the same is called symmetrical. The line which divides the shape is called the symmetry. So, if we place a mirror

• ### Measuring the Line Segment | Comparing Line Segments

We will discuss here about measuring the line segment i.e. how to draw and measure a line segment using scale or ruler. We can measure a line segment by two ways. (i) With the help of scale

• ### Perimeter of a Triangle | Perimeter of a Triangle Formula | Examples

We will discuss here how to find the perimeter of a triangle. We know perimeter of a triangle is the total length (distance) of the boundary of a triangle. Perimeter of a triangle is the sum of lengths of its three sides. The perimeter of a triangle ABC Perimeter

• ### Perimeter of a Rectangle | How to Find the Perimeter of a Rectangle?

We will discuss here how to find the perimeter of a rectangle. We know perimeter of a rectangle is the total length (distance) of the boundary of a rectangle. ABCD is a rectangle. We know that the opposite sides of a rectangle are equal. AB = CD = 5 cm and BC = AD = 3 cm

• ### Perimeter of a Square | How to Find the Perimeter of Square? |Examples

We will discuss here how to find the perimeter of a square. Perimeter of a square is the total length (distance) of the boundary of a square. We know that all the sides of a square are equal. Perimeter of a Square Perimeter of the square ABCD = AB+BC+CD+AD=2 cm+2cm+2cm+2cm

• ### Mental Math on Geometrical Shapes | Geometry Worksheets| Answer

In mental math on geometrical shapes we will solve different type of problems on simple closed curves, polygons, basic geometrical concepts, perpendicular lines, parallel lines, circle, terms relates to circle, relation between radius and diameter of a circle, symmetry

Related Concepts on Geometry - Simple Shapes & Circle

Simple Closed Curves

Polygon

Different Types of Polygons

Angle

Triangle

Circle Math

Line Symmetry

Symmetrical Shapes

4th Grade Math Activities

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

## Recent Articles

1. ### What is a Triangle? | Types of Triangle | Scalene Triangle | Isosceles

Jun 17, 24 11:22 PM

A simple closed curve or a polygon formed by three line-segments (sides) is called a triangle. The above shown shapes are triangles. The symbol of a triangle is ∆. A triangle is a polygon with three s…

2. ### Interior and Exterior of an Angle | Interior Angle | Exterior Angle

Jun 16, 24 05:20 PM

Interior and exterior of an angle is explained here. The shaded portion between the arms BA and BC of the angle ABC can be extended indefinitely.

3. ### Angles | Magnitude of an Angle | Measure of an angle | Working Rules

Jun 16, 24 04:12 PM

Angles are very important in our daily life so it’s very necessary to understand about angle. Two rays meeting at a common endpoint form an angle. In the adjoining figure, two rays AB and BC are calle

4. ### What is a Polygon? | Simple Closed Curve | Triangle | Quadrilateral

Jun 16, 24 02:34 PM

What is a polygon? A simple closed curve made of three or more line-segments is called a polygon. A polygon has at least three line-segments.