What is a line of symmetry?
Year 4 identifies lines of symmetry in 2D shapes in different orientations and completes symmetric figures. Below: what it means, a worked example, the mistake to watch for and an 11+ question.
The answer
A line of symmetry splits a shape into two halves that are mirror images of each other.
What it means
If you fold a shape along a line of symmetry, the two halves match exactly. That is why it is also called a mirror line.
A square has 4 lines of symmetry, a rectangle has 2, an equilateral triangle has 3 and a circle has an endless number.
A worked example
How many lines of symmetry does an isosceles triangle have?
- Fold it from the top corner, between the two equal sides, to the middle of the opposite side.
- The halves match. No other fold works, so it has 1 line of symmetry.
The common mistake
Thinking a rectangle's diagonals are lines of symmetry. Fold a rectangle along a diagonal and the corners do not meet: it only has 2 lines, across the middle each way.
How it comes up in the 11+
How many lines of symmetry does a regular octagon have?
Answer: 8
- A regular polygon has as many lines of symmetry as it has sides.
- 4 lines go through opposite corners and 4 through the middles of opposite sides: 8 altogether.
Related words and practice
More maths words
Questions parents ask
Does a circle have lines of symmetry?
Yes, an endless number. Any straight line through the centre splits it into two matching halves.
Is rotational symmetry the same thing?
No. Rotational symmetry is about turning a shape, not folding it. It is not in the primary curriculum, but some 11+ papers include it.
Knowing the words is half of an 11+ maths question
11+ papers use maths vocabulary without explaining it. The free diagnostic checks maths, English and both kinds of reasoning, and shows what to practise next. No card is required.