Class 6 Maths Chapter 9 Symmetry (NCERT Ganita Prakash) – Concepts, Examples and Complete Solutions
Class 6 Maths Chapter 9: Symmetry
Ganita Prakash – NCERT Explained
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:
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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
c) Square or circle
Why Symmetry is Important
Symmetry is widely used in:
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Architecture
-
Art and design
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Engineering
-
Nature patterns
-
Computer graphics
Learning symmetry also improves visual thinking and creativity.
Quick Summary
In this chapter we learned:
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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:
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Folding paper shapes
-
Drawing mirror images
-
Observing patterns in nature
Try drawing your own symmetric designs at home.
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