O Level MathematicsC4.5 Symmetry (line and rotational).
🪞 Mastering Symmetry: Lines & Spins!
Edudent Academy
7 Jan 26
Symmetry pops up everywhere – from perfectly cut snowflakes to the elegant logos in your favourite apps. **Understanding symmetry** helps O-Level students quickly recognise patterns, check constructions, and score marks in geometry questions.
Core Ideas to Remember
- Line symmetry (reflectional): A shape has a line of symmetry if it can be folded along a line and both halves match exactly.
- Rotational symmetry: A shape has rotational symmetry of order if it fits onto itself times in one full turn.
- The smallest angle of rotation is
Worked Example: Regular Hexagon
Problem: A regular hexagon is drawn on paper. Determine (a) the number of lines of symmetry, and (b) the order of rotational symmetry about its centre.
Step 1: Visualise or sketch the hexagon – all sides and angles are equal.
Step 2: Lines of symmetry – draw a line through each pair of opposite vertices (3 lines) and through the mid-points of opposite sides (3 more). Total lines: **6**.
Step 3: Rotational symmetry – the shape maps onto itself every turn.
Answer: The regular hexagon has 6 lines of symmetry and rotational symmetry of order 6. Keep practising with other polygons to strengthen your intuition!
Step 1: Visualise or sketch the hexagon – all sides and angles are equal.
Step 2: Lines of symmetry – draw a line through each pair of opposite vertices (3 lines) and through the mid-points of opposite sides (3 more). Total lines: **6**.
Step 3: Rotational symmetry – the shape maps onto itself every turn.
Answer: The regular hexagon has 6 lines of symmetry and rotational symmetry of order 6. Keep practising with other polygons to strengthen your intuition!