GEOMETRY

Symmetry

Learn the reliable method for symmetry, then apply it to 11+ exam-style questions.

1 · WHAT YOU NEED TO KNOW

The idea

A line of symmetry divides a shape into matching mirror halves.

Picture itMatch both sides across the mirror line
2 · THE METHOD

Follow these steps

  1. Test a possible mirror line.
  2. Check that corresponding points are equally far from the line.
  3. Distinguish reflection symmetry from rotational symmetry.
3 · WORKED EXAMPLES

See the method in action

Example 1

How many lines of symmetry does this regular 6-sided polygon have?

  1. Half the symmetry lines pass through opposite vertices and half through the midpoints of opposite sides: 3 + 3 = 6.
Answer: 6
Example 2

How many lines of symmetry does this regular 10-sided polygon have?

  1. Half the symmetry lines pass through opposite vertices and half through the midpoints of opposite sides: 5 + 5 = 10.
Answer: 10
4 · ELEVENSPRINT TIP

A useful shortcut

Distinguish reflection symmetry from rotational symmetry.

5 · COMMON MISTAKES

Watch out for these

6 · TRY IT YOURSELF

Three fresh questions

Ready to check the method? You will get three fresh, validated questions.