Table of Contents
- The Line of Symmetry
- The Line of Symmetry for Different Geometric Shapes
- How can we find whether a Shape has a Line of Symmetry or not?
- How can we find the “Number” of Lines of Symmetry?
- How do we Draw the Lines of Symmetry for a Shape?
- What are Symmetric Shapes?
- How can we Draw a Symmetric Shape?
- Solved Examples
- Frequently Asked Questions
What is Lines of Symmetry?
The axis or imaginary line that passes through the centre of the shape or object, and divides it into identical halves is known as the line of symmetry.
The Line of Symmetry for Different Geometric Shapes
Triangles:
A triangle can have 3, 1, or no lines of symmetry.
Quadrilaterals:
The number of the lines of symmetry varies, and this depends on the type of quadrilateral.
Circle:
A circle has an infinite number of lines of symmetry because an infinite number of lines can be drawn passing through its centre.
How Can We Find Whether a Shape has a Line of Symmetry or not?
Folding Test:
Folding a shape reveals whether or not it has a line of symmetry.
The fold line becomes the line of symmetry when the folded parts sit perfectly on top of each other, with all the edges matching.
Let us try folding a rectangle in one way, but it didn’t work out.
However, when we try it in another way, in which the folded parts sit perfectly on top of each other with all the edges matching, it works!
This is because the rectangle has been folded along its line of symmetry, to get two perfectly equal folds.
How Can We Find the “Number” of Lines of Symmetry?
Let us look at an example to understand the manner in which we can find the number of lines of symmetry for a specific shape.
Example 1:
In the given figure we will need to calculate the number of lines of symmetry.
Solution:
In the given figure, there are 6 lines of symmetry and these are denoted by the letters a, b, c, d, e, and f.
How Do We Draw the Lines of Symmetry for a Shape?
In the given figure, we check whether the figure can be divided into identical halves, so that the line of symmetry can be drawn. Then we draw the line of symmetry between these two halves.
Let us consider an example to understand how we can draw a line of symmetry for a shape.
Example 2:
Draw all the lines of symmetry for this shape.
Solution:
Look for two halves of this shape that are mirror images of each other, to draw a line of symmetry. Then, draw a line of symmetry between these two halves.
The upper half of the D is mirrored in the bottom half. As a result, the horizontal line that runs through the center of the D is the line of symmetry.
There are no other options for splitting this shape into halves that are mirror images of one another. So, this is the only line of symmetry.
What are Symmetric Shapes?
If a shape can be divided through the center such that two identical pieces are formed, the shape is said to be symmetric.
How Can We Draw a Symmetric Shape?
A symmetric shape has identical parts that mirror each other across the line of symmetry.
Let us take an example to understand how we can draw a symmetric shape.
For example, one half of the symmetrical shape is given. Draw the rest of the shape.
First, create a line of symmetry.
On the other side of the line of symmetry, draw the other half of the shape.
Solved Examples on Symmetry Lines
Example 1:
Check for the line symmetry in the shape that is given in the diagram.
Solution:
The shape can be folded in a manner that the two halves are perfectly aligned.
There is only one line of symmetry in the shape. As a result, the shape has one line of symmetry.
Example 2:
Check for the line of symmetry in this shape.
Solution:
The shape cannot be folded in a manner that the two halves are perfectly aligned.
As a result, there is no line of symmetry in the shape.
Example 3:
A standard rectangular piece of paper catches Ria’s eye. Assist her in using the properties of the line of symmetry to calculate the number of the lines of symmetry.
Solution:
Only two lines of symmetry, I and m, are present.
You may think that the diagonal lines are also the lines of symmetry. However, when you reflect a rectangle along the diagonal, you never get an identical mirror image that overlaps each other perfectly with matching edges.
Example 4:
As shown in the diagram, this is one half of a symmetrical shape. Complete the shape by drawing the rest of it.
Solution:
Method 1:
First, create a line of symmetry.
On the other side of the line of symmetry, draw the other half of the shape.
Method 2:
First, create a line of symmetry.
On the other side of the line of symmetry, draw the other half of the shape.
Example 5:
This image depicts one half of a symmetrical shape, a butterfly. Complete the shape.
Solution:
First, create a line of symmetry.
On the other side of the line of symmetry, draw the other half of the shape.
A line of symmetry is an imaginary line or axis along which you can fold a shape or figure to get symmetrical halves. It is also known as the symmetry axis. The line of symmetry is also known as a mirror line because it breaks a shape into two identical reflections of an image.
Symmetrical shapes or figures are objects that can have a line drawn through them, so that the images on both sides of the line mirror each other.
The lines of symmetry need to pass through the center of the figure. Hence, they intersect at the center. Intersecting lines cannot be parallel. Therefore, it is not possible for the lines of symmetry to be parallel to each other.
Figures or shapes have lines of symmetry when they can be divided into two halves through the line of symmetry.