Fun with Symmetry — Class 4 Mathematics (CBSE)

From the current NCERT Maths Mela Grade 4 book, Chapter 11. Symmetry is the beauty of matching halves — in shapes, letters, and nature.

1. Why this chapter matters

Many things around us — leaves, butterflies, rangoli, and letters — are symmetrical. Learning about lines of symmetry and reflection helps us see patterns, draw neatly, and understand shapes better.

2. Core ideas

Idea 1 — Symmetry means matching halves

A shape is symmetrical if it can be folded so the two halves match exactly. The fold line is the line of symmetry.

Method 2 — Test by folding or with a mirror

Fold the shape, or place a mirror on the line — if the reflection completes the shape, it is symmetrical.

Skill 3 — Some shapes have more than one line of symmetry

A square has 4 lines, a rectangle has 2, a circle has many, and an equilateral triangle has 3.

3. Worked examples

Example 1: Is a butterfly shape symmetrical? How many lines?

Yes — folding down the middle makes the wings match. It has 1 line of symmetry.

Example 2: How many lines of symmetry does a square have?

4 lines (two through the middles of the sides, two along the diagonals).

Example 3: Is the letter A symmetrical? Is R?

A is symmetrical (1 vertical line). R is not symmetrical.

4. Activity corner

Fold and cut paper to make a symmetrical shape (a heart, a leaf, a butterfly). Then draw half a simple figure and complete the other half to make it symmetrical. Write:

• The shape you made and its line(s) of symmetry
• How you checked (fold or mirror)
• The maths idea (matching halves)

5. Common mistakes

• Mistake: Calling a shape symmetrical when the halves do not match. Fix: Fold or use a mirror — the halves must match exactly.
• Mistake: Thinking every shape has only one line of symmetry. Fix: A square has 4, a rectangle 2, a circle many.
• Mistake: Drawing the second half unevenly. Fix: Reflect each point the same distance on the other side of the line.

6. How to write better answers

1. Decide if the shape is symmetrical (fold or mirror test).
2. Draw and count the line(s) of symmetry.
3. To complete a figure, reflect each part across the line.
4. State your answer clearly.

7. Practice set

1. What is a line of symmetry?
2. How many lines of symmetry does a square have?
3. How many lines of symmetry does a rectangle have?
4. Is the letter H symmetrical?
5. Name one object in nature that is symmetrical.
6. Does a circle have one or many lines of symmetry?

8. Answer key

1. The fold line where the two halves of a shape match exactly.
2. 4 lines.
3. 2 lines.
4. Yes, the letter H is symmetrical.
5. A leaf, a butterfly, or a flower (answers may vary).
6. Many lines of symmetry.

9. Quick revision

• A symmetrical shape has two halves that match when folded.
• The fold line is the line of symmetry; a mirror shows the reflection.
• Square: 4 lines; rectangle: 2; circle: many; equilateral triangle: 3.
• Some shapes have no line of symmetry (like the letter R).
• To complete a figure, reflect each part across the line.