Class 6 Maths Chapter 9 Symmetry NCERT Solutions (Concepts, Step-by-Step Answers & Examples | Ganita Prakash Complete Guide)

📘 Class 6 Ganita Prakash Chapters

• Chapter 1: Knowing Our Numbers
• Chapter 2: Lines and Angles
• Chapter 3: Whole Numbers
• Chapter 4: Data Handling
• Chapter 5: Prime Time
• Chapter 6: Perimeter and Area
• Chapter 7: Fractions
• Chapter 8: Playing with Constructions
• Chapter 9: Symmetry
• Chapter 10: The Other Side of Zero

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Introduction

Symmetry is one of the most beautiful ideas in mathematics. We see symmetry everywhere around us: in butterflies, flowers, buildings, rangoli patterns, and even in letters of the alphabet.

In this chapter, students learn how shapes can be divided into equal halves and how patterns repeat in a balanced way.

Understanding symmetry helps students develop strong observation skills and is an important concept in geometry.

In this article by FUZY MATH ACADEMY, we will learn:

• What symmetry means
• Line of symmetry
• Symmetry in alphabets and shapes
• Reflection symmetry
• Step-by-step NCERT solutions

What is Symmetry?

A figure is said to be symmetrical if it can be folded into two identical halves.

If both halves match exactly when folded, the figure has symmetry.

Example:

Butterfly wings show symmetry because the left and right sides are mirror images.

Line of Symmetry

A line of symmetry is a line that divides a figure into two identical parts.

When a figure is folded along this line, both parts coincide perfectly.

Example:

A square has 4 lines of symmetry.

Examples of objects with symmetry:

• Leaf

• Butterfly

• Star

• Flower

Symmetry in Geometrical Shapes

Different shapes have different numbers of lines of symmetry.

Shape	Lines of Symmetry
Circle	Infinite
Square	4
Rectangle	2
Equilateral Triangle	3
Isosceles Triangle	1

This helps students visually understand balance in shapes.

Symmetry in Alphabets

Some English letters also show symmetry.

Vertical Symmetry

Letters that can be divided vertically:

A, M, T, U, V, W, Y

Horizontal Symmetry

Letters with horizontal symmetry:

B, C, D, E, K

Both Horizontal and Vertical

H
I
O
X

Reflection Symmetry

Reflection symmetry means one half of a figure is the mirror image of the other half.

Think of a mirror placed at the center of a figure.

Whatever appears on one side appears exactly on the other side.

Example:

Human face
Butterfly
Leaf

Example Problem

Question

Identify the number of lines of symmetry in a rectangle.

Solution

Step 1: Observe the rectangle carefully.

Step 2: Draw a vertical line through the center.

Both halves match exactly.

Step 3: Draw a horizontal line through the center.

Again both halves match.

Step 4: Check diagonal lines.

They do NOT divide the rectangle into identical halves.

Final Answer

A rectangle has 2 lines of symmetry.

Example Problem 2

Question

Does a circle have a line of symmetry?

Solution

Step 1: Draw any straight line through the center of the circle.

Step 2: Fold along the line.

Step 3: Both halves coincide perfectly.

Step 4: This can be done with infinite lines passing through the center.

Final Answer

A circle has infinitely many lines of symmetry.

Practice Questions (From NCERT)

Question 1

Which letters of the English alphabet have line symmetry?

Solution

Examples include:

A, H, I, M, O, T, U, V, W, X, Y

Students can check this by folding paper along the middle.

Question 2

Draw a figure that has:

a) One line of symmetry
b) Two lines of symmetry
c) More than two lines of symmetry

Solution

a) Isosceles triangle

b) Rectangle

c) Square or circle

Why Symmetry is Important

Symmetry is widely used in:

• Architecture

• Art and design

• Engineering

• Nature patterns

• Computer graphics

Learning symmetry also improves visual thinking and creativity.

Quick Summary

In this chapter we learned:

• Meaning of symmetry

• Line of symmetry

• Symmetry in shapes and alphabets

• Reflection symmetry

• Practice questions with solutions

Students who clearly understand symmetry find geometry much easier in higher classes.

Practice Tip from FUZY MATH ACADEMY

The best way to learn symmetry is by:

• Folding paper shapes

• Drawing mirror images

• Observing patterns in nature

Try drawing your own symmetric designs at home.

 

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Previous Chapter: Chapter 8 – Playing with Constructions
Next Chapter: Chapter 10 – The Other Side of Zero

Q1. What is symmetry?

Symmetry means a figure looks the same when parts are repeated in a definite pattern. Example: a butterfly has reflection symmetry.

Q2. What is a line of symmetry?

A line of symmetry divides a figure into two mirror halves. Folding along this line makes both halves overlap exactly.

Q3. How many lines of symmetry does a square have?

A square has 4 lines of symmetry: vertical, horizontal, and two diagonals.

Q4. Does a rectangle have diagonal symmetry?

No, only a square has diagonal symmetry. A rectangle has 2 lines of symmetry (vertical and horizontal).

Q5. What is reflection symmetry?

Reflection symmetry means one half of a figure is the mirror image of the other half across a line of symmetry.

Q6. What is rotational symmetry?

Rotational symmetry means a figure looks the same after rotation about a fixed point by certain angles.

Q7. What is the centre of rotation?

The fixed point about which a figure is rotated to check rotational symmetry is called the centre of rotation.

Q8. How many angles of symmetry does a square have?

A square has 4 angles of symmetry: 90°, 180°, 270°, and 360°.

Q9. What is the order of rotational symmetry?

The number of times a figure coincides with itself during a full 360° rotation is called its order of rotational symmetry.

Q10. What symmetry does a circle have?

A circle has infinite lines of symmetry and infinite angles of rotational symmetry because it looks the same at any rotation.

Q11. How many lines of symmetry does an equilateral triangle have?

An equilateral triangle has 3 lines of symmetry, each passing through a vertex and the midpoint of the opposite side.

Q12. How many lines of symmetry does a regular hexagon have?

A regular hexagon has 6 lines of symmetry and rotational symmetry of order 6.

Q13. Can a figure have reflection symmetry but no rotational symmetry?

Yes. Example: the letter "A" has reflection symmetry but no rotational symmetry.

Q14. Can a figure have rotational symmetry but no reflection symmetry?

Yes. Example: a pinwheel has rotational symmetry but no reflection symmetry.

Q15. What symmetry does the Ashoka Chakra have?

The Ashoka Chakra has 24 lines of symmetry and rotational symmetry of order 24.