Maths

Symmetry

Class 4

🎯 Learning Objectives

📖 Let Us Begin!

Have you ever folded a rangoli design in half and noticed that both sides look the same? That is symmetry. When you fold a shape along a special line and both halves match perfectly, the shape is called symmetrical. The fold line is called the line of symmetry.

Symmetry is everywhere -- in flowers, butterflies, buildings like the Taj Mahal, and even in the letters of the English alphabet.

A Friendly Introduction

Have you ever folded a rangoli design in half and noticed that both sides look the same? That is symmetry. When you fold a shape along a special line and both halves match perfectly, the shape is called symmetrical. The fold line is called the line of symmetry.

Symmetry is everywhere -- in flowers, butterflies, buildings like the Taj Mahal, and even in the letters of the English alphabet.

What Is Symmetry?

A figure has symmetry if it can be divided into two halves that are mirror images of each other. The line that divides the figure is called the line of symmetry (also called the mirror line).

If you place a mirror along the line of symmetry, the reflection looks exactly like the other half.

Think: Fold a piece of paper in half and cut a shape. When you open it, both sides match -- that is symmetry!

Lines of Symmetry in Shapes

Different shapes have different numbers of lines of symmetry.

ShapeLines of SymmetryNote
CircleInfinite (countless)Any line through the centre is a line of symmetry
Square42 diagonal + 1 vertical + 1 horizontal
Rectangle21 vertical + 1 horizontal (diagonals are not lines of symmetry)
Equilateral Triangle3One from each vertex to the opposite side
Isosceles Triangle1Only one vertical line through the top vertex
Think: Why does a rectangle not have a diagonal line of symmetry, but a square does?

Symmetry in English Capital Letters

Some English capital letters are symmetrical. Here are a few examples:

LetterVertical Line of SymmetryHorizontal Line of Symmetry
AYesNo
HYesYes
MYesNo
OYesYes
TYesNo
XYesYes

Letters like H, O, and X have both vertical and horizontal lines of symmetry. Letters like A, M, and T have only a vertical line of symmetry.

Symmetry in Nature

Nature is full of beautiful symmetrical patterns:

Example
Example 1: Butterfly

A butterfly has one vertical line of symmetry. The left wing is a mirror image of the right wing. If you see a butterfly in a garden in Kerala or Assam, notice how both wings have the same colours and patterns.

Example
Example 2: Leaf

Many leaves, such as a peepal leaf or a mango leaf, have one line of symmetry running along the central vein. The left half mirrors the right half.

📝 Key Words

WordMeaning
SymmetryWhen two halves of a figure match exactly
Line of SymmetryThe line along which a figure can be folded so both halves overlap perfectly
Mirror LineAnother name for the line of symmetry
SymmetricalA figure that has at least one line of symmetry
AsymmetricalA figure that has no line of symmetry
⭐ Key Points to Remember

✏️ Practice Questions

A. Fill in the Blanks
1. A figure that can be divided into two matching halves has .
2. The line along which we fold a figure to get matching halves is called the .
3. A square has lines of symmetry.
4. A rectangle has lines of symmetry.
5. A circle has lines of symmetry.
B. True or False
1. The letter B has a vertical line of symmetry.
2. A butterfly has one line of symmetry.
3. A rectangle has 4 lines of symmetry.
4. The letter X has both vertical and horizontal lines of symmetry.
C. How Many Lines of Symmetry?
1. Equilateral triangle:
2. Letter H:
3. Letter T:
4. Isosceles triangle:
D. Multiple Choice Questions
1. Which shape has exactly 2 lines of symmetry?
(a) Square(b) Circle(c) Rectangle(d) Equilateral triangle
2. Which letter has NO line of symmetry?
(a) A(b) H(c) F(d) O
3. A butterfly shows symmetry with how many lines of symmetry?
(a) 0(b) 1(c) 2(d) 4
E. Short Answer
1. Write any three capital letters that have a vertical line of symmetry.
2. Why does a circle have infinite lines of symmetry? Explain in one sentence.
3. Draw the other half of a symmetrical figure: Imagine the left half of a leaf is given. Describe how you would complete the right half.
🎨 Fun Activity -- Ink Blot Symmetry

Take a sheet of white paper. Fold it in half. Open it and drop a few drops of ink or paint on one side of the fold. Now fold the paper again and press gently. Open it up and see the beautiful symmetrical pattern you have created.

Paste or describe your ink blot pattern below:

Where is the line of symmetry in your ink blot?

Want to use this as a worksheet? Switch to the A4 printable view.

Mathematics -- Class 4

Topic: Symmetry
Name: ____________________________Class: 4Date: ________________
Learning Objectives
A Friendly Introduction

Have you ever folded a rangoli design in half and noticed that both sides look the same? That is symmetry. When you fold a shape along a special line and both halves match perfectly, the shape is called symmetrical. The fold line is called the line of symmetry.

Symmetry is everywhere -- in flowers, butterflies, buildings like the Taj Mahal, and even in the letters of the English alphabet.

What Is Symmetry?

A figure has symmetry if it can be divided into two halves that are mirror images of each other. The line that divides the figure is called the line of symmetry (also called the mirror line).

If you place a mirror along the line of symmetry, the reflection looks exactly like the other half.

Think: Fold a piece of paper in half and cut a shape. When you open it, both sides match -- that is symmetry!

Lines of Symmetry in Shapes

Different shapes have different numbers of lines of symmetry.

ShapeLines of SymmetryNote
CircleInfinite (countless)Any line through the centre is a line of symmetry
Square42 diagonal + 1 vertical + 1 horizontal
Rectangle21 vertical + 1 horizontal (diagonals are not lines of symmetry)
Equilateral Triangle3One from each vertex to the opposite side
Isosceles Triangle1Only one vertical line through the top vertex

Think: Why does a rectangle not have a diagonal line of symmetry, but a square does?

Symmetry in English Capital Letters

Some English capital letters are symmetrical. Here are a few examples:

LetterVertical Line of SymmetryHorizontal Line of Symmetry
AYesNo
HYesYes
MYesNo
OYesYes
TYesNo
XYesYes

Letters like H, O, and X have both vertical and horizontal lines of symmetry. Letters like A, M, and T have only a vertical line of symmetry.

Symmetry in Nature

Nature is full of beautiful symmetrical patterns:

Example 1: Butterfly

A butterfly has one vertical line of symmetry. The left wing is a mirror image of the right wing. If you see a butterfly in a garden in Kerala or Assam, notice how both wings have the same colours and patterns.

Example 2: Leaf

Many leaves, such as a peepal leaf or a mango leaf, have one line of symmetry running along the central vein. The left half mirrors the right half.

Key Words
WordMeaning
SymmetryWhen two halves of a figure match exactly
Line of SymmetryThe line along which a figure can be folded so both halves overlap perfectly
Mirror LineAnother name for the line of symmetry
SymmetricalA figure that has at least one line of symmetry
AsymmetricalA figure that has no line of symmetry

Mathematics -- Class 4 (continued)

Topic: Symmetry -- Key Points and Practice
Key Points to Remember
Practice Questions

A. Fill in the Blanks

  1. A figure that can be divided into two matching halves has .
  2. The line along which we fold a figure to get matching halves is called the .
  3. A square has lines of symmetry.
  4. A rectangle has lines of symmetry.
  5. A circle has lines of symmetry.

B. True or False

  1. The letter B has a vertical line of symmetry.
  2. A butterfly has one line of symmetry.
  3. A rectangle has 4 lines of symmetry.
  4. The letter X has both vertical and horizontal lines of symmetry.

C. How Many Lines of Symmetry?

  1. Equilateral triangle:
  2. Letter H:
  3. Letter T:
  4. Isosceles triangle:

D. Multiple Choice Questions

  1. Which shape has exactly 2 lines of symmetry?
    (a) Square(b) Circle(c) Rectangle(d) Equilateral triangle
  2. Which letter has NO line of symmetry?
    (a) A(b) H(c) F(d) O
  3. A butterfly shows symmetry with how many lines of symmetry?
    (a) 0(b) 1(c) 2(d) 4

E. Short Answer

  1. Write any three capital letters that have a vertical line of symmetry.
  2. Why does a circle have infinite lines of symmetry? Explain in one sentence.
  3. Draw the other half of a symmetrical figure: Imagine the left half of a leaf is given. Describe how you would complete the right half.
Fun Activity -- Ink Blot Symmetry

Take a sheet of white paper. Fold it in half. Open it and drop a few drops of ink or paint on one side of the fold. Now fold the paper again and press gently. Open it up and see the beautiful symmetrical pattern you have created.

Paste or describe your ink blot pattern below:

Where is the line of symmetry in your ink blot?