PW Class 6 Maths Notes Chapter 9: Symmetry
Neha Tanna5 Sept, 2026
Some shapes can be divided into matching parts, while others look exactly the same even after they are turned. These properties are examples of symmetry, which can be seen in geometric shapes as well as objects around us.
PW Class 6 Symmetry Notes help you understand how symmetry works through lines, reflections, and rotations. You will study the line of symmetry, reflection symmetry, rotational symmetry, the order of rotational symmetry, and the special symmetry of a circle.
What Is Symmetry?
Symmetry is a characteristic of an object or shape that allows it to be divided into two or more identical parts. These parts may be mirrored or rotated around a fixed point or axis.
Symmetry can be seen in both natural and man-made objects. Butterfly wings, a human face, mandala patterns, and architectural designs are some examples where matching parts can be observed.
What Is a Line of Symmetry?
A line of symmetry is an imaginary line that divides a shape into two identical halves.
If you fold a shape along its line of symmetry, the two halves overlap perfectly. Depending on the shape, the line can be vertical, horizontal, or diagonal.
Different shapes can have different numbers of lines of symmetry:
| Shape | Lines of Symmetry |
| Equilateral Triangle | 3 |
| Square | 4 |
| Hexagon | 6 |
| Dodecagon | 12 |
| Isosceles Triangle | 1 |
| Rectangle | 2 |
| Parallelogram | 0 |
| Circle | Infinite |
For example, a square has four lines of symmetry. These include its two diagonals and two perpendicular bisectors. A circle has infinitely many lines of symmetry because it can be folded along any line passing through its centre.
What Is Reflection Symmetry?
Reflection symmetry, also called mirror symmetry, occurs when one half of an object is the mirror image of the other half. For reflection symmetry to occur, a line of symmetry divides the object into two identical parts.
A butterfly is a simple example. Its two wings can show reflection symmetry, with one wing appearing as the mirror image of the other. A human face can also show reflection symmetry when divided down the middle.
The key idea is to look at the two sides of the line of symmetry and see whether they form matching mirror images.
What Is Rotational Symmetry?
A shape has rotational symmetry when it can be rotated around a central point by less than a full circle and still look exactly the same. As the shape turns, it may match its original position more than once. The number of times this happens during one complete rotation is called its order of rotational symmetry.
How Does Rotational Symmetry Work in a Regular Hexagon?
A regular hexagon matches its original shape at:
60°, 120°, 180°, 240°, 300°, and 360°
This gives it an order of rotational symmetry of 6.
How Does Rotational Symmetry Work in a Square?
A square matches its original shape at:
90°, 180°, 270°, and 360°
Its order of rotational symmetry is 4.
These examples show that different shapes can return to their original appearance a different number of times during one full rotation.
What Symmetries Does a Circle Have?
A circle has some special symmetry properties.
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Infinite Lines of Symmetry
A circle has infinitely many lines of symmetry. You can draw a line through its centre in any direction, and it will divide the circle into two identical halves.
This means there is no single vertical, horizontal, or diagonal line that gives a circle its symmetry. Any line passing through the centre can work as a line of symmetry.
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Rotational Symmetry of Infinite Order
A circle also has rotational symmetry of infinite order because it continues to look the same when rotated through any angle.
For example, rotating a circle by 1°, 90°, or 180° does not change its appearance. It still matches its original shape.
PW Class 6 Maths Notes Chapter 9: Symmetry PDF
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How Can PW Class 6 Notes Help You Understand Symmetry?
The PW Class 6 Symmetry Notes keep the different types of symmetry separate while also showing how they are connected. This can make it easier to identify what kind of symmetry a shape has.
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Spot Lines of Symmetry with PW
Use the PW notes to see how an imaginary line can divide a shape into two identical halves. You can also compare shapes such as a square, rectangle, triangle, and circle to see how the number of symmetry lines can change.
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Understand Mirror Symmetry with PW
Reflection symmetry becomes easier to recognise when you look for two matching halves. Examples such as a butterfly can help you connect the idea of a line of symmetry with a mirror image.
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Follow Rotations with PW
When revising rotational symmetry, focus on whether a shape matches its original position after being turned. The square and regular hexagon examples help you see how the matching angles determine the order of rotational symmetry.
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Compare the Two Symmetries of a Circle
A circle is useful for comparing both ideas in one shape. With PW, you can revisit why a circle has infinite lines of symmetry as well as rotational symmetry of infinite order.
Complete PW Resources for Class 6 Maths Preparation
You can use these PW Class 6 Maths resources to revise other chapters, practise questions, and prepare for exams.
| PW Class 6 Resource | How It Can Help You |
| PW Class 6 Maths Notes | Revise concepts and topics from other Class 6 Maths chapters. |
| PW Class 6 Maths Syllabus | See all the Maths chapters you will study in Class 6. |
| PW Class 6 Most Important Questions | Practise important questions from different Maths chapters. |
| PW Class 6 Sample Papers | Solve different types of Maths questions and prepare for exams. |
Symmetry helps you recognise how parts of a shape can match through a line, reflection, or rotation. A square can have both line and rotational symmetry, while a circle takes these ideas further with infinite symmetry. PW Class 6 Symmetry Notes help you keep these ideas clear and revise their examples before moving on to practice questions.
