What is a line of symmetry?
A line of symmetry is an imaginary line that cuts a shape into two identical parts — like a mirror: what you see on one side is exactly the same on the other side, just flipped.
The dashed line is a line of symmetry: the left and right sides are identical
Checking with folding
The most reliable test is folding: if you cut out the shape and fold it along the line, the two parts should match up exactly, edge to edge. That's why a line of symmetry is sometimes called a "fold line".
One, several or no symmetry
The number of lines of symmetry depends on the shape:
- A rectangle (non-square) has 2 lines of symmetry (horizontal and vertical).
- A square has 4 lines of symmetry (2 like the rectangle, plus the 2 diagonals).
- A circle has an infinite number of lines: any diameter is one.
- An equilateral triangle (3 equal sides) has 3 lines of symmetry.
- Some shapes, like the letter F or a scalene triangle, have no line of symmetry at all.
Drawing a mirror image on squared paper
To draw the mirror image of a shape across a line (often a line on the grid), work point by point:
- Choose a point on the original shape.
- Count how many squares separate it from the line.
- Mark the same number of squares, but on the other side of the line, on the same row (perpendicular to the line).
- Repeat for every key point of the shape (usually the corners), then join the points in the same order.
Mistakes to avoid
- Confusing symmetry with simple similarity: two identical shapes that aren't mirror-aligned are not symmetrical.
- Miscounting the squares when placing a point on the other side of the line.
- Forgetting the perpendicular distance to the line must be kept, not the diagonal distance.
- Assuming every shape has a line of symmetry: many don't.
Worked exercises
How many lines of symmetry does a square have?
A point is 3 squares to the left of the line. Where should its mirror image go?
Does an equilateral triangle have a line of symmetry?
Now it's your turn!
On EasyMaths, your child practises recognising and drawing symmetrical shapes with kind marking, for free.
Start the exercises →Frequently asked questions
What is a line of symmetry?
It's an imaginary line that splits a shape into two identical parts, as if you folded a piece of paper in half: the two halves match up exactly.
How do you check a shape has a line of symmetry?
The simplest test is folding: if you fold the shape along the line and the two parts match up exactly, the line is a line of symmetry. On squared paper, you can also count the squares on each side.
Can a shape have more than one line of symmetry?
Yes! A square has 4 lines of symmetry, a circle has an infinite number. Other shapes, like the letter F, have none at all.