Learning Objectives
- Identify lines of symmetry in different shapes
- Understand rotational symmetry and order of rotation
- Distinguish between line symmetry and rotational symmetry
Key Concepts
Line Symmetry (Reflection Symmetry)
A figure has line symmetry if it can be folded along a line so that the two halves match exactly. This line is called the line of symmetry or axis of symmetry.
A figure can have one, two, multiple, or no lines of symmetry.
- Equilateral triangle: 3 lines of symmetry
- Square: 4 lines of symmetry
- Circle: Infinite lines of symmetry
- Rectangle: 2 lines of symmetry
Rotational Symmetry
A figure has rotational symmetry if it looks the same after being rotated less than 360° about its centre.
Order of rotational symmetry = Number of times the figure looks the same during a complete 360° rotation.
Angle of rotation = 360° ÷ Order
- Equilateral triangle: order 3, angle 120°
- Square: order 4, angle 90°
- Regular hexagon: order 6, angle 60°
Summary
Symmetry is about balanced proportions. Line symmetry involves a mirror line that divides a shape into two identical halves. Rotational symmetry means a shape looks the same after rotation by a certain angle. Many shapes have both types of symmetry.
Important Terms
- Line of Symmetry
- A line that divides a figure into two mirror-image halves
- Rotational Symmetry
- Property where a figure looks the same after rotation by less than 360°
- Order of Rotation
- The number of times a shape fits onto itself during one full turn
- Centre of Rotation
- The fixed point around which the figure rotates
Quick Revision
- A regular polygon of n sides has n lines of symmetry and order n rotational symmetry
- Every figure has rotational symmetry of order 1 (360° rotation)
- A circle has infinite lines of symmetry
- Letters like A, M, U have vertical line symmetry
- Some shapes have rotational symmetry but no line symmetry (e.g., S, Z)
Practice Tips
- Cut out shapes from paper and fold them to find lines of symmetry
- Use a pin to rotate shapes and count the order of rotational symmetry
- Look for symmetry in everyday objects, letters, and nature