🪞 Symmetry
Symmetry is all around us — in butterflies, letters, buildings and shapes. Let's learn about lines of symmetry and rotational symmetry!
🪞 Line Symmetry
A shape has line symmetry (also called reflective symmetry) when you can fold it exactly in half and both halves match perfectly. The fold line is called the line of symmetry.
Circle
Infinite lines of symmetry
Rectangle
2 lines of symmetry
Isosceles Triangle
1 line of symmetry
Test for symmetry: fold the shape. If both halves match exactly — it has a line of symmetry!
🔢 How Many Lines?
Many shapes have more than one line of symmetry. A regular shape with n sides has n lines of symmetry.
| Shape | Lines of Symmetry | Notes |
|---|---|---|
| Equilateral triangle | 3 | All sides equal |
| Square | 4 | 2 through sides, 2 through corners |
| Rectangle (not square) | 2 | Through midpoints of sides only |
| Regular hexagon | 6 | 6 equal sides |
| Scalene triangle | 0 | All sides different |
🔄 Rotational Symmetry
A shape has rotational symmetry if it looks the same after being rotated (turned) less than a full turn around its centre. The number of times it matches during a full turn is the order of rotational symmetry.
Regular pentagon star
Order 5 — looks the same 5 times in a full turn
Square
Order 4 — looks the same at 90°, 180°, 270°, 360°
Scalene triangle
Order 1 — only matches once (full turn)
Every shape has at least order 1 rotational symmetry — it matches itself after a full 360° turn.
Worked Examples
Example 1: Lines of symmetry in the letter A
The capital letter A has 1 line of symmetry — a vertical line down the middle.
Letter A: 1 line of symmetry ✅
Example 2: Does a rectangle have rotational symmetry?
A rectangle looks the same after a 180° turn — it has rotational symmetry of order 2.
Rectangle: rotational symmetry order 2 ✅
Example 3: Symmetry in nature
A butterfly has 1 line of reflective symmetry (down the middle of its body). It does not have rotational symmetry of order more than 1.
Butterfly: 1 line of symmetry, rotational order 1 ✅
Key Vocabulary
A fold line that divides a shape into two identical halves.
When one half of a shape is a mirror image of the other half.
When a shape looks the same after being rotated less than 360°.
How many times a shape matches itself in one full 360° rotation.
Knowledge Check
Question 1: How many lines of symmetry does a square have?
Question 2: Which shape has NO line of symmetry?
Question 3: An equilateral triangle has how many lines of symmetry?
Question 4: A square has rotational symmetry of order:
Question 5: The letter H — how many lines of symmetry does it have?
Pax Says:
"Look for symmetry at home — in tiles, windows, leaves and butterflies! Fold paper shapes to test them. How many lines of symmetry can you find?"
Key Concepts Summary
- ✓ A line of symmetry divides a shape into two identical mirror halves.
- ✓ A regular polygon with n sides has n lines of symmetry.
- ✓ Rotational symmetry means a shape looks the same after being turned less than 360°.
- ✓ The order of rotational symmetry tells you how many times the shape matches in a full rotation.