# Symmetry

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 1 What is Symmetry? 2 Line of Symmetry 3 Shapes with more than One Line of Symmetry 4 Thinking out of the Box! 5 Reflection and Rotational Symmetry 6 Point Symmetry 7 Important Notes on Symmetry 8 Examples of Symmetry 9 Fun Facts on Symmetry 10 Practice Questions on Symmetry 11 Maths Olympiad Sample Papers 12 Frequently Asked Questions (FAQs) 13 FREE Worksheets on Symmetry

## What is Symmetry?

### Symmetry: Definition

An object has a symmetry if it can be divided into two identical pieces.

When an object has a symmetry, we say that it is symmetrical.

If an object does not have a symmetry, we say that the object is asymmetrical.

The concept of symmetry is commonly found in geometry.

The following images are symmetrical.

## Line of Symmetry

The line of symmetry is a line that divides an object into two identical pieces.

Here, we have a star and we can fold it into two equal halves.

If you fold a figure in half along its line of symmetry, you will notice that both the halves match each other exactly.

This line of symmetry is called the axis of symmetry.

The line of symmetry is vertical if it cuts the shape from top to bottom and vice-versa.

The line of symmetry is horizontal if it cuts the shape from right to left and vice-versa.

Sometimes, we can split a shape across the corners to form two identical halves.

In such a case, the line of symmetry is diagonal.

Now its time to explore the symmetrical shapes visually.

Mark one line of symmetry by selecting the points

## Shapes with more than one Line of Symmetry

Some symmetrical figures have a single line of symmetry while others have more than one.

Consider this triangle.

It has only one line of symmetry.

If you try to divide it any other way, the parts will be asymmetrical.

In comparison to the above triangle, the one shown below has 3 lines of symmetry.

Number of lines of symmetry Examples of figures
No line of symmetry Scalene triangle
Exactly one line of symmetry Isosceles triangle
Exactly two lines of symmetry Rectangle
Exactly three lines of symmetry Equilateral triangle

### Making a Symmetrical Figure: Ink String Patterns

Let us do a simple activity.

Dip short lengths of strings in different coloured paints or inks.

Now, place these strings on half of a paper.

Fold the paper and press the two halves.

Pull out the strings from the paper.

Is the resulting figure symmetric?

If yes, what is the line of symmetry?

Try out more such patterns!

Think Tank

 1. The designs on the playing cards have a line of symmetry. Can you identify them for the following cards? 2. Can you list the letters in the English alphabet from A to Z that have no lines of symmetry?

## Reflection and Rotational Symmetry

### Reflection Symmetry

When one half of an object is exactly the same as the other half of the object, it has reflection symmetry.

It can be observed that the two halves are reflections of each other.

Some human faces are identical on the left and right sides.

Reflection of mountains and trees in clear water is an example of reflection symmetry.

### Rotational Symmetry

Look at this starfish.

This starfish has 5 lines of symmetry that meet at a point P.

We can rotate the starfish about the point P.

If you turn or rotate the starfish about the point P, it will still look the same from all directions.

This kind of symmetry is called rotational symmetry.

The famous ferris wheel, the London Eye, is an example of rotational symmetry.

You can find many objects in real life that have rotational symmetry like wheels, windmills, road-signs, ceiling fans and so on.

Let's play with some figures having reflection and rotational symmetry.

Symmetry is everywhere around us.

Almost all plants, animals, and even humans are symmetric.

## Point Symmetry

An object has a point symmetry if every part of the object has a matching part.

Many letters of the English alphabet have a point symmetry.

The point O is the central point and the matching parts are in opposite directions.

If an object looks the same when you turn it upside down, then it is said to have a point symmetry.

The shape and the matching parts must be in opposite directions.

Important Notes
1. All regular polygons are symmetrical in shape. The number of lines of symmetry is the same as the number of its sides.
2. An object and its image are symmetrical with reference to its mirror line.
3. If a figure has a rotational symmetry of $$180^{\circ}$$, then it has a point symmetry.

## Examples of Symmetry

### Symmetry in Real Life

 Example 1

Symmetry is often found in nature.

One common example is a butterfly.

When a butterfly folds its wings, it is easy to observe symmetry in its wings.

The wings of most of the butterflies are identical on the left and right sides.

 Example 2

Symmetry is one of the most prevalent themes in art, architecture, and design.

Do you know why these architectural marvels of India are beautiful?

This is because of symmetry!

Thus, the geometry and the symmetry of the structure gives uniqueness to these monuments.

 Example 3

Observe this beautiful figure.

Symmetric shapes and patterns appear more beautiful than non-symmetric ones.

This is Koch’s Snowflake.

It has a symmetrical pattern.

You can find many similar, beautiful objects that have symmetry in real life.

## Symmetry: Fun Facts

A kaleidoscope has mirrors inside it that produces images that have multiple lines of symmetry.

The angle between the mirror decides the number of lines of symmetry.

We may have observed several symmetrical objects in our daily life like rangolis or kolams.

The striking aspect of symmetry can be observed in rangoli designs.

These designs are famous in India for their unique and symmetrical patterns.

They depict the colourful science of symmetry.

## Practice Questions

Here are a few activities for you to practice. Select/Type your answer and click the "Check Answer" button to see the result.

IMO (International Maths Olympiad) is a competitive exam in Mathematics conducted annually for school students. It encourages children to develop their math solving skills from a competition perspective.

## 1. What is symmetry in math?

When an object is exactly the same when you turn it or flip it, that object has a symmetry.

Symmetrical objects are of the same size and shape.

## 2. What are the 4 types of symmetry?

The main four types of symmetry are rotational symmetry, reflectional symmetry, point symmetry and translational symmetry.

## 3. What is symmetry? Explain with an example.

Symmetry Definition: When an object is exactly the same when you turn it or flip it, that object has a symmetry.

Symmetrical objects are of the same size and shape.

Nature has plenty of objects having symmetry.

Some common examples for symmetry are shown below.

## 4. What is a symmetric pattern?

All patterns having a symmetry are called symmetric patterns.

Leaves of plants have various patterns and shapes. Most of these leaves depict symmetric patterns.

For example, the two sides of a leaf look similar with respect to their shape, size and structure.

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