Five pictures depicting examples of line symmetry in our daily life

What is Symmetry?

Look at these two images of butterflies. What difference do you see?

Symmetry

The first butterfly looks exactly the same from both the left and right sides while the second butterfly does not look the same from the left and right sides.

The images which can be divided into identical halves are called symmetrical. The images that cannot be divided into identical halves are asymmetrical.

You must have seen the following symmetrical objects in your surroundings:

Symmetrical objects

Line of symmetry

Any line splitting a shape into two parts such that the two parts are the same is called a line of symmetry. These parts are also said to be symmetrical to each other.

For instance, the image below shows a line of symmetry which splits the red outlined shape into two parts that are exactly the same.

Line of symmetry

Line of symmetry 1

Based on the above examples, we obtain the following observations:

The sides of the image split up by the line of symmetry, must look the same[c].
If we fold the paper (on which image is drawn) along the line of symmetry, each part of the image will completely overlap the other part.

The above observations will help us find the line of symmetry in any shape.

Example 1: Which of the following shapes does not have a line of symmetry?

Find the line of symmetry in any shape

Solution:

If we fold both the papers from top to down as shown in A1 and B1, we get a line of symmetry in A but not in B. If we fold both the papers from left to right as shown in A2 and B2, we get no line of symmetries in both A and B.

Find the line of symmetry in any shape 1

Shapes with more than one lines of symmetry

Can we have more than one line of symmetry? The answer is yes. The table below shows some examples of shapes/figures with more than one line of symmetry.