Symmetry (Grade 4)
When you fold a shape in half and both halves match exactly, the shape has symmetry. The fold line is called the line of symmetry.
In Class 4, you will learn to find lines of symmetry in shapes, letters, and everyday objects. You will also learn that some shapes have more than one line of symmetry.
What is Symmetry - Class 4 Maths (Geometry)?
A shape has line symmetry (or reflection symmetry) if a line can divide it into two halves that are mirror images of each other.
The line that divides the shape is called the line of symmetry (or axis of symmetry). When you fold the shape along this line, the two halves overlap perfectly.
Types and Properties
Lines of symmetry in common shapes:
| Shape | Lines of Symmetry |
|---|---|
| Circle | Infinite (any line through the centre) |
| Square | 4 |
| Rectangle | 2 |
| Equilateral Triangle | 3 |
| Isosceles Triangle | 1 |
| Scalene Triangle | 0 |
| Regular Pentagon | 5 |
| Regular Hexagon | 6 |
Rule: A regular polygon with n sides has n lines of symmetry.
Some shapes have no lines of symmetry — for example, a parallelogram (that is not a rectangle or rhombus) and a scalene triangle.
Solved Examples
Example 1: Example 1: Line of symmetry in a square
Problem: How many lines of symmetry does a square have?
Solution:
Step 1: A square can be folded along the vertical centre line — both halves match. (Line 1)
Step 2: It can be folded along the horizontal centre line. (Line 2)
Step 3: It can be folded along one diagonal. (Line 3)
Step 4: It can be folded along the other diagonal. (Line 4)
Answer: A square has 4 lines of symmetry.
Example 2: Example 2: Rectangle symmetry
Problem: How many lines of symmetry does a rectangle (not a square) have?
Solution:
Step 1: Fold along the vertical centre line — left half matches right half. ✓
Step 2: Fold along the horizontal centre line — top half matches bottom half. ✓
Step 3: Fold along a diagonal — the halves do NOT overlap perfectly. ✗
Answer: A rectangle has 2 lines of symmetry.
Example 3: Example 3: Symmetry in English letters
Problem: Which of these letters have a vertical line of symmetry: A, B, C, M, S?
Solution:
Step 1: A — fold vertically down the middle → left matches right. ✓
Step 2: B — the left side is straight, right side is bumpy → not symmetrical vertically. ✗
Step 3: C — not symmetrical vertically. ✗ (It has horizontal symmetry.)
Step 4: M — fold vertically → left matches right. ✓
Step 5: S — no vertical or horizontal symmetry. ✗
Answer: A and M have a vertical line of symmetry.
Example 4: Example 4: Equilateral triangle
Problem: How many lines of symmetry does an equilateral triangle have?
Solution:
Step 1: An equilateral triangle has 3 equal sides.
Step 2: A line from each vertex to the midpoint of the opposite side is a line of symmetry.
Step 3: There are 3 such lines.
Answer: An equilateral triangle has 3 lines of symmetry.
Example 5: Example 5: No symmetry
Problem: Does a scalene triangle have any line of symmetry?
Solution:
Step 1: A scalene triangle has all three sides of different lengths.
Step 2: No matter where you fold it, the two halves will not match.
Answer: A scalene triangle has 0 lines of symmetry.
Example 6: Example 6: Symmetry in a butterfly
Problem: Priya observes a butterfly with its wings spread. Does it show symmetry?
Solution:
Step 1: Draw an imaginary line along the body of the butterfly (from head to tail).
Step 2: The left wing mirrors the right wing.
Answer: Yes, a butterfly has 1 line of symmetry — a vertical line through its body.
Example 7: Example 7: Completing a symmetric shape
Problem: Half of a shape is drawn on the left side of a vertical line. The left side shows a triangle. Draw the other half to make it symmetric.
Solution:
Step 1: Each point on the left side must have a matching point on the right side, at the same distance from the line.
Step 2: Mirror the triangle — same shape, same size, flipped across the line.
Answer: The completed shape is a symmetric figure (like an arrow or diamond depending on the triangle).
Example 8: Example 8: Circle symmetry
Problem: How many lines of symmetry does a circle have?
Solution:
Step 1: Any line through the centre of a circle divides it into two equal halves.
Step 2: There are infinitely many such lines (vertical, horizontal, diagonal, and every angle in between).
Answer: A circle has infinite lines of symmetry.
Example 9: Example 9: Symmetry in rangoli
Problem: Meera makes a rangoli pattern shaped like a regular hexagon. How many lines of symmetry does it have?
Solution:
Step 1: A regular hexagon has 6 equal sides.
Step 2: A regular polygon with n sides has n lines of symmetry.
Step 3: n = 6, so there are 6 lines of symmetry.
Answer: The rangoli has 6 lines of symmetry.
Real-World Applications
Symmetry is found in nature, art, and design:
- Human body — left side roughly mirrors the right side.
- Butterflies and leaves — natural symmetry.
- Rangoli and kolam — Indian art patterns use symmetry.
- Architecture — the Taj Mahal is a famous example of symmetric design.
- Logos and flags — many national flags have lines of symmetry.
Key Points to Remember
- A shape has symmetry if it can be folded into two matching halves.
- The fold line is the line of symmetry.
- A square has 4 lines of symmetry. A rectangle has 2.
- An equilateral triangle has 3. An isosceles triangle has 1. A scalene triangle has 0.
- A circle has infinite lines of symmetry.
- A regular polygon with n sides has n lines of symmetry.
- Some shapes (like a parallelogram that is not a rectangle) have no line of symmetry.
Practice Problems
- Find the number of lines of symmetry in the letters: H, T, O, N, X.
- How many lines of symmetry does a rhombus have?
- Draw an isosceles triangle and show its line of symmetry.
- Does a parallelogram (not a rectangle or rhombus) have a line of symmetry?
- Aman says the letter Z has a line of symmetry. Is he correct?
- Draw half of a shape on one side of a line and complete the other half to make it symmetric.
- Name three objects in your home that have at least one line of symmetry.
Frequently Asked Questions
Q1. What is a line of symmetry?
A line of symmetry divides a shape into two halves that are exact mirror images. When you fold the shape along this line, both halves overlap perfectly.
Q2. Can a shape have more than one line of symmetry?
Yes. A square has 4 lines of symmetry, an equilateral triangle has 3, and a circle has infinitely many.
Q3. Does every shape have a line of symmetry?
No. Scalene triangles, parallelograms (that are not rectangles or rhombuses), and irregular shapes may have no lines of symmetry.
Q4. How many lines of symmetry does a rectangle have?
A rectangle (that is not a square) has exactly 2 lines of symmetry — one vertical and one horizontal through the centre.
Q5. Is the diagonal of a rectangle a line of symmetry?
No. If you fold a rectangle along its diagonal, the two halves do not match. Diagonals are lines of symmetry only in a square and a rhombus.
Q6. What is the difference between symmetry and pattern?
Symmetry means a shape can be folded into two matching halves. A pattern is a repeated design, which may or may not be symmetric.
Q7. Where do we see symmetry in nature?
Butterflies, flowers, leaves, snowflakes, starfish, and the human face all show symmetry.
Q8. How do you check if a shape is symmetric?
Try folding it (or imagine folding it) along a line. If the two halves match exactly, the shape is symmetric along that line.
