Symmetry

A shape has line symmetry if you can fold it so both halves match exactly. It has rotational symmetry if it looks the same after turning less than a full turn.

Key facts

  • A mirror line splits a shape into two matching halves.
  • Order of rotational symmetry: how many times it looks the same in one full turn.
  • A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.

Worked examples

Example 1

How many lines of symmetry does a rectangle have?

  1. Fold top to bottom: matches.
  2. Fold left to right: matches.
  3. Folding along a diagonal does not match, so there are 2.

Answer: 2

Example 2

What is the order of rotational symmetry of a regular pentagon?

  1. It looks the same after every fifth of a turn (72°).
  2. That happens 5 times in a full turn.

Answer: 5