Sheet № 209 · Foundation + Higher · AQA · Edexcel · OCR
Symmetry: Lines and Rotational –
Symmetry is a fundamental GCSE Maths topic tested at both Foundation and Higher tiers. Questions ask you to identify lines of symmetry, state the order of rotational symmetry for a shape, or complete a pattern given a mirror line or centre of rotation. This guide explains both types of symmetry clearly, provides worked examples, and gives
§Key definitions
Symmetry
describes how a shape can be mapped onto itself by a reflection or rotation.
Question:
State the number of lines of symmetry and the order of rotational symmetry of a regular pentagon.
Answer:
5 lines of symmetry and rotational symmetry of order 5.
Q1 (Foundation):
How many lines of symmetry does a rhombus have?
Q2 (Foundation):
State the order of rotational symmetry of the letter "S".
§Formulas to memorise
A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n
Line symmetry (reflective symmetry): — A shape has line symmetry if you can draw a line — called a mirror line or line of symmetry — so that one half is a perfect reflection of the other.
Symmetry: describes how a shape can be mapped onto itself by a reflection or rotation.
Worked example
State the number of lines of symmetry and the order of rotational symmetry of a regular pentagon.
Working:
⚠ Common mistakes
- ✗Counting order 0 for rotational symmetry. The minimum order is always 1 — every shape maps onto itself after a full 360° turn.
- ✗Missing diagonal lines of symmetry. Students often find horizontal and vertical mirror lines but forget to check diagonals, especially in squares and rhombuses.
- ✗Confusing a parallelogram's rotational symmetry with line symmetry. A parallelogram has order 2 rotational symmetry but no lines of symmetry.
✦ Exam tips
- →Use tracing paper in the exam to test rotational symmetry — trace the shape, pin the centre, and rotate.
- →For completing a shape given a mirror line, measure each point's perpendicular distance from the line and plot the same distance on the other side.
- →Regular polygon questions are predictable: n sides always gives n lines of symmetry and order n.
- →Read the question carefully — "how many lines of symmetry" and "order of rotational symmetry" are different things.