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CBSE Notes
Class 6
Maths
Chapter 9 Symmetry

Cbse Class 6 Maths Notes Chapter 9 Symmetry

Symmetry is an interesting concept that plays a crucial role in CBSE Class 6 Maths, art, nature, and even in our daily lives. In simple terms, symmetry refers to the balanced and proportional arrangement of parts on either side of a central point or axis. It helps us understand how shapes and objects can be mirrored, rotated, or reflected in different ways. In this blog, we’ll explore the different types of symmetry, including Line of Symmetry, Reflection, Rotational Symmetry, and the Symmetries of a Circle.

1.0What is Symmetry?

Symmetry can be described as the characteristic of an object or shape that allows it to be divided into two or more identical parts. These parts can either be mirrored or rotated around a fixed point or axis. Symmetry can be observed in various natural and man-made objects, from the wings of butterflies to the architectural designs of buildings.

Examples showing symmetry

2.0Line of Symmetry

The Line of Symmetry is an imaginary line that splits a shape into two identical halves. If you fold a shape along this line, the two halves will overlap perfectly. This line can be vertical, horizontal, or diagonal, depending on the shape.

  • For example, a square has four lines of symmetry (two diagonals and two perpendicular bisectors), whereas a circle has infinite lines of symmetry because it can be folded along any line passing through its centre.

Example:

Image showing lines of symmetry

3.0Reflection Symmetry

Reflection symmetry, also known as mirror symmetry, occurs when one half of an object is a mirror image of the other half. This is possible when there is a line of symmetry dividing the object into two identical parts.

  • Real-life example: The human face exhibits reflection symmetry when divided down the middle.

Example showing Reflection symmetry

  • A butterfly’s wings also show reflection symmetry, where each wing is a mirror image of the other.

Reflection symmetry is common in many natural forms and shapes, where the two halves mirror each other across a central line.

4.0Rotational Symmetry

A shape has rotational symmetry if it can be rotated (less than a full circle) around a central point and still look exactly the same. The number of times a shape can fit into its original position during a complete rotation is called its order of rotational symmetry.

  • For example, a regular hexagon has 6 lines of rotational symmetry, because it can be rotated by 60°, 120°, 180°, 240°, 300°, and 360°, and it will still look the same at each of these positions.
  • A regular square has 4 lines of rotational symmetry, as it matches its original shape at 90°, 180°, 270°, and 360° rotations.

Image showing the example of rotation symmetry

5.0Symmetries of a Circle

  • A circle is a special shape that exhibits infinite lines of symmetry. This means that you can draw a line through the centre of the circle in any direction, and the two halves will always be identical. The symmetry of a circle is a perfect example of how the concept of symmetry extends to continuous shapes.
  • A circle also exhibits rotational symmetry of infinite order because it can be rotated by any angle, and it will always appear the same. Whether you rotate a circle by 1°, 90°, or 180°, the circle remains unchanged.
  • This infinite symmetry makes the circle a unique and fundamental shape in geometry and real-world design.

6.0Applications of Symmetry

Symmetry isn’t just an abstract concept; it has real-world applications in various fields:

  • Art and Architecture: Symmetry plays a vital role in designing visually pleasing structures, from classical buildings to modern skyscrapers. The Parthenon in Greece is a perfect example of symmetry in architecture.
  • Nature: The symmetry found in flowers, leaves, animal bodies, and even galaxies showcases the beauty of natural designs.
  • Engineering: Symmetry helps in designing efficient mechanical parts and structures, such as gears and wheels, ensuring balance and strength.

7.0Benefits of CBSE Notes for Class 6 Maths Chapter 9 - Symmetry

  • Practice Questions and Solutions: Many CBSE Notes include practice questions with solutions, allowing you to test your understanding and identify areas where you need more practice.
  • Time-Saving: Instead of going through the entire NCERT Solutions textbook, notes provide a summarised version of the chapter, saving you valuable study time.
  • Improved Problem-Solving Skills: By understanding the core concepts through the notes, you can approach problem-solving in a more structured and confident way.
  • Better Exam Preparation: Comprehensive CBSE Notes for Class 6 Maths ensure you are well-prepared for your exams by covering all the essential topics and types of questions.
  • Building a Strong Foundation: A solid understanding of symmetry in CBSE Class 6 forms a crucial foundation for more advanced geometry concepts in higher classes.

Chapter-wise CBSE Notes for Class 6 Maths:

Class 6 Maths Chapter 1 - Patterns In Mathematics Notes

Class 6 Maths Chapter 2 - Lines And Angles Notes

Class 6 Maths Chapter 3 - Number Play Notes

Class 6 Maths Chapter 4 - Data Handling And Presentation Notes

Class 6 Maths Chapter 5 - Prime Time Notes

Class 6 Maths Chapter 6 - Perimeter And Area Notes

Class 6 Maths Chapter 7 - Fractions Notes

Class 6 Maths Chapter 8 - Playing With Constructions Notes

Class 6 Maths Chapter 9 - Symmetry Notes

Class 6 Maths Chapter 10 - The Other Side Of Zero Notes


Chapter-wise NCERT Solutions for Class 6 Maths:

Chapter 1: Patterns in Mathematics

Chapter 2: Lines and Angles

Chapter 3: Number Play

Chapter 4: Data Handling and Presentation

Chapter 5: Prime Time

Chapter 6: Perimeter and Area

Chapter 7: Fractions

Chapter 8: Playing With Construction

Chapter 9: Symmetry

Chapter 10: The Other Side of Zero

Frequently Asked Questions

Symmetry is when an object or shape can be divided into two identical parts that are mirror images of each other.

There are two main types of symmetry: Reflection symmetry (Mirror symmetry): When one half of an object is a mirror image of the other half. Rotation symmetry: When an object can be rotated around a point and still look the same.

A line of symmetry is an imaginary line that divides a shape into two identical halves. Each half is a mirror image of the other.

To find the line of symmetry, fold the shape along the potential line and check if both halves match exactly.

An object has rotational symmetry if it can be rotated around a central point by a certain angle and still look the same.

Yes, some shapes have more than one line of symmetry. For example, a square has four lines of symmetry.

Common examples of symmetry in real life include: Butterflies (Reflection symmetry) Snowflakes (Reflection symmetry) Clock faces (Rotational symmetry)

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