Symmetry (Edexcel GCSE Maths): Revision Notes
Symmetry
Lines of symmetry
Line of symmetry is also known as a mirror line. When you have a line of symmetry, one half of the shape appears as an exact mirror image of the other half.
To identify lines of symmetry, imagine folding the shape along a potential line. If both halves match up perfectly when folded, then you have found a line of symmetry.
Examples: Lines of Symmetry in Different Shapes
Shapes can have different numbers of lines of symmetry:
- No lines of symmetry: Some shapes, like the L-shaped figure, cannot be folded along any line to create matching halves
- One line of symmetry: The letter Y has exactly one vertical line of symmetry down its centre
- Two lines of symmetry: A rectangle has two lines of symmetry - one horizontal and one vertical through its centre
- Four lines of symmetry: A cross shape has four lines of symmetry - two through its centre (horizontal and vertical) and two diagonal lines
Using Tracing Paper Technique
In your GCSE exam, you can ask for tracing paper to help identify lines of symmetry. Here's how to use it effectively:
- Place tracing paper over the shape and trace it carefully
- Fold the tracing paper along a potential line of symmetry
- If the two halves match up exactly when folded, you've found a line of symmetry
- Repeat this process to find all possible lines of symmetry
Rotational symmetry
A shape has rotational symmetry when it fits exactly over itself after being rotated through a certain angle. The order of rotational symmetry tells you how many times the shape matches its original position during one complete 360° turn.
Understanding rotational symmetry
When checking for rotational symmetry, you rotate the shape around its centre point. If the shape looks identical to its starting position at certain points during the rotation, it has rotational symmetry.
Examples: Different Orders of Rotational Symmetry
Different shapes have different orders of rotational symmetry:
- No rotational symmetry: An L-shaped figure only matches its original position once during a full turn
- Order 2: A Z-shaped figure fits over itself twice - once at 180° and once at 360°
- Order 3: A three-armed shape fits over itself three times during a complete turn
- Order 4: A cross shape fits over itself four times - at 90°, 180°, 270°, and 360°
Using Tracing Paper for Rotational Symmetry
Tracing paper is also useful for checking rotational symmetry:
- Trace the shape onto the paper
- Place the tracing over the original shape
- Rotate the tracing paper around the centre point
- Count how many times the traced shape fits exactly over the original during one complete turn
- This count gives you the order of rotational symmetry
For example, if a shape fits over itself at 180° and 360°, it has rotational symmetry of order 2.
Exam Tips
- Always use tracing paper when available - it makes identifying symmetry much more accurate
- Take your time when rotating or folding to ensure precise alignment
- Remember that all shapes have at least rotational symmetry of order 1 (they match themselves at 360°)
- Look for obvious symmetries first, then check for less obvious ones
- Practice with different shapes to build confidence in recognising symmetry patterns
Key Points to Remember:
- Line of symmetry creates mirror images when you fold along it
- Rotational symmetry means the shape fits over itself when rotated
- Order tells you how many times a shape matches during one full turn
- Tracing paper is your best friend for checking both types of symmetry accurately
- All shapes have at least rotational symmetry of order 1