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Line Symmetry – Definition, Types, Examples

Key Concepts

  • Line of symmetry
  • Types of lines of symmetry
  • Draw shapes with line symmetry

Introduction:  

 Symmetry 

A shape is said to be symmetric if it can be divided into two identical pieces which are placed in an organised way. 

Fig 1 (Introduction to the symmetry)

Line Symmetry 

A figure is line-symmetric if it can be folded on a line to form two matching parts that fit exactly on top of each other. The fold line is called a line symmetry. 

Fig 2 (Line symmetry)

A real-life example 

Fig 3 (Veins of a leaf)

Types of lines of symmetry 

A line of symmetry is an axis along which an object, when cut, will have identical halves. These objects might have one, two, or multiple lines of symmetry. 

  • One line of symmetry 
  • Two lines of symmetry 
  • Infinite lines of symmetry 

One line of symmetry 

Shapes or figures with one line of symmetry are symmetrical only about one axis. It may be horizontal, vertical or diagonal. 

Fig 4 (Alphabet A has one line of symmetry)

Two lines of symmetry 

Shapes or figures with two lines of symmetry are symmetrical only about two lines. The lines may be vertical, horizontal or diagonal lines. 

Fig 5 (A rectangle has two lines of symmetry)

Infinite lines of symmetry 

Shapes or figures with infinite lines of symmetry are symmetrical only about two lines. The lines may be vertical, horizontal, or diagonal lines. 

Fig 6 (A circle has infinite lines of symmetry)

The following table shows the examples for different shapes with the number of lines of symmetry that they have. 

table

Line symmetry 

Example 1 

Sarah wants to design a line-symmetric tabletop. She sketched half of the tabletop. How can Sarah complete her design? 

Fig 7 (Symmetrical shape on a plane)

Step1: Draw a line of symmetry as shown in the figure. 

Fig 8 (Half symmetrical shape on a plane)

Step2: Complete Sarah’s design on the opposite side of the line of symmetry. 

Fig 9 (Full symmetrical shape on a plane) 

Example 2 

A square has 4 lines of symmetry 

Fig 10 (Square shape symmetry) 

Example 3 

A triangle has 3 lines of symmetry 

Fig 11 (Triangle symmetry)

Exercise:

  1. How many lines of symmetry these major geometry shapes have?
1
  1. How many lines of symmetry the given figure has?
2
  1. How many lines of symmetry do we in numbers from 0 To 9 have?
  2. Draw the lines of symmetry for the following figures
3
  1. Identify the shapes given below. Check whether they are symmetric or not. Draw the line of symmetry as well
5
  1. Trace each figure and draw the lines of symmetry, if any:
6
  1. List any four symmetrical shapes from your home or school.
  2. Draw a hexagon with 6 lines of symmetry.
  3. Draw all the letters of English alphabets which has no lines of symmetry.
  4. Draw a triangle which has:

(a) exactly one line of symmetry?                   (b) exactly two lines of symmetry?

(c) exactly three lines of symmetry?             (d) no lines of symmetry?

What we have learnt:

  • Recognize and define lines, line segments and rays
  • Understand parallel and perpendicular lines
  • Understand triangles based on angles
  • Understand triangles based on sides
  • Learn quadrilaterals and classification of quadrilaterals
  • Solve questions based on lines, angles and shapes

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