Symmetry

In this chapter, there is a simpler explanation of symmetry. Symmetry is when something is perfectly balanced and one side is like a mirror image of the other side. It's like having a twin but in the world of shapes!

Symmetry

Symmetry is like a special kind of balance and sameness in a shape. It means that one side of an object looks just like the other side when you split it in half.

The figure shows symmetric and asymmetric objects.

Line of Symmetry

The line of symmetry is the imaginary line or axis that you draw around a figure to make it symmetrical. The line of symmetry can be vertical, horizontal or diagonal. There may be one or more lines of symmetry.

Imagine folding a piece of paper in half. If both sides match perfectly, that is symmetry! The line where you fold it is called the ‘line of symmetry’.

This figure shows the lines of symmetry of a leaf, an apple and a butterfly.

There is one line of symmetry for digit 3 and two lines of symmetry for the digits 0 and 8. Other digits such as 1, 2, 4, 5, 6, 7 and 9 have no line of symmetry.

The lines of symmetry of alphabet are shown below:

The lines of symmetry of some figures are shown below:

Example: How many lines of symmetry does the alphabet "X" have?

a) No line of symmetry
b) One line of symmetry
c) Two lines of symmetry
d) Three lines of symmetry

Answer: c) Two lines of symmetry

Explanation: The alphabet “X” has two lines of symmetry, shown as:

Rotational Symmetry

Rotational symmetry is a geometric phenomenon in which the shape of an object is symmetrical when rotated on its vertical axis. This symmetry can be observed when the object is rotated 180° or when it is rotated with certain angles either in a clockwise or an anticlockwise manner.

Have you ever seen something that looks the same even when you turn it? That is called "rotational symmetry." It's like when you spin a wheel and it looks the same as it turns.

The figure shows a clockwise rotation of 180°.

Centre of Rotation

The centre of rotation is a fixed point around which rotational symmetry occurs in a figure or object.

To understand rotational symmetry, we need to know about the "centre of rotation". This is like the point where something turns or spins. Imagine you have a drawing on a paper and you stick a pin right in the middle of it. That pin is the centre of rotation.

Centre of rotation of a wheel is shown as follows:

Order of Rotational Symmetry

The order of symmetry is the number of times a figure can be moved around and still look the same as it did before it was moved. This tells us how many times something looks the same as you turn it around the centre.

Let’s learn more about the order of rotation.

Order 1: If something looks the same only once as you turn it 360°, it has "order 1" rotational symmetry.

The arrow looks the same only once after 360° rotation. Therefore, the order of symmetry is one.

Order 2: If something looks the same two times as you turn it 180 degrees each time, it has "order 2" rotational symmetry.

A rectangle looks the same after you turn it halfway and then again after another half-turn. It looks the same after 180° rotation. Therefore, the order of symmetry is two.

Example: What is the order of rotational symmetry for a kite?

a) Order 1
b) Order 2
c) Order 3
d) Order 4

Answer: a) Order 1

Explanation: The order of rotational symmetry for a kite is 1.

The order of symmetry is the number of times a figure can be moved around and still look the same as it did before it was moved.

In this question, the kite looks the same only once after 360° rotation. Therefore, the order of symmetry is one. 

The rotation clockwise is shown as:

The rotation anticlockwise is shown as: