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)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5738.png)
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)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5737.png)
A real-life example
![Fig 3 (Veins of a leaf)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5739.png)
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)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5745.png)
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)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5740.png)
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)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5746.png)
The following table shows the examples for different shapes with the number of lines of symmetry that they have.
![table](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5747.png)
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)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5742.png)
Step1: Draw a line of symmetry as shown in the figure.
![Fig 8 (Half symmetrical shape on a plane)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5741.png)
Step2: Complete Sarah’s design on the opposite side of the line of symmetry.
![Fig 9 (Full symmetrical shape on a plane)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5743.png)
Example 2
A square has 4 lines of symmetry
![Fig 10 (Square shape symmetry)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5748.png)
Example 3
A triangle has 3 lines of symmetry
![Fig 11 (Triangle symmetry)](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5744.png)
Exercise:
- How many lines of symmetry these major geometry shapes have?
![1](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5749.png)
- How many lines of symmetry the given figure has?
![2](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5750.png)
- How many lines of symmetry do we in numbers from 0 To 9 have?
- Draw the lines of symmetry for the following figures
![3](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5751.png)
- Identify the shapes given below. Check whether they are symmetric or not. Draw the line of symmetry as well
![5](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5752.png)
- Trace each figure and draw the lines of symmetry, if any:
![6](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5753.png)
- List any four symmetrical shapes from your home or school.
- Draw a hexagon with 6 lines of symmetry.
- Draw all the letters of English alphabets which has no lines of symmetry.
- 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
Concept Map
![Concept Map](https://www.turito.com/learn-internal/wp-content/uploads/2022/09/image-5754.png)
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