Line symmetry
Fold a butterfly along a straight line down its middle and the two wings land exactly on top of each other. Fold a heart, a maple leaf, the letter M — the two halves match. That straight line is called an axis of symmetry (or "line of symmetry"), and a shape that has one is line-symmetric.
The fold test
The easiest way to check whether a shape is line-symmetric is the paper-fold test:
- Cut the shape out of paper.
- Fold it along a straight line.
- If the two halves fit on top of each other perfectly — same outline, no gaps, no overhang — the fold is an axis of symmetry.
If you can't find a fold where the halves match, the shape has no axis of symmetry. Lots of everyday objects have no symmetry — a hand, a number 4, the letter F.
What an axis of symmetry does
An axis of symmetry acts like a mirror.
- Every point on one side has a partner on the other side.
- Both partners are the same distance from the axis.
- The line that joins them crosses the axis at a right angle.
This is why we sometimes call the axis a mirror line — looking at one half is exactly like looking at the other half in a mirror.
Some shapes have more than one axis
| Shape | Number of axes |
|---|---|
| scalene triangle | 0 |
| isosceles triangle | 1 (down the middle) |
| equilateral triangle | 3 (from each vertex to the opposite side) |
| rectangle | 2 (horizontal and vertical) |
| square | 4 (2 across the middle + 2 diagonals) |
| regular pentagon | 5 |
| circle | infinitely many (every diameter is an axis) |
A regular polygon with n sides has n axes of symmetry. The more sides, the more axes — until a circle has so many that every diameter works.
⚠️ The two diagonals of a rectangle are not axes of symmetry, unless the rectangle happens to be a square. Many children get this wrong because the diagonal cuts the rectangle in half — but the two halves don't match when you fold along it.
What you will learn
- Lines of symmetry — how to find them and count them
- Completing a symmetric figure — drawing the missing half
- Symmetry around us — letters, leaves, flags, signs
- For parents — practical games at home