What is symmetry?
A shape has line symmetry if you can fold it along a line and both halves match exactly.
That fold line is called a line of symmetry (or mirror line).
Examples
A square has 4 lines of symmetry
- 1 vertical, 1 horizontal, and 2 diagonal
A rectangle has 2 lines of symmetry
- 1 vertical and 1 horizontal (but not diagonal — try it!)
An equilateral triangle has 3 lines of symmetry
- One from each corner to the middle of the opposite side
A circle has infinite lines of symmetry
- Any line through the centre is a line of symmetry
- The picture only shows a few examples because we can’t draw infinitely many lines on one diagram
Shapes with no symmetry
Some shapes, like a scalene triangle (all sides different) or a parallelogram (that isn’t a rectangle), have zero lines of symmetry.
How to check
- Imagine folding the shape along the line
- Would both halves overlap perfectly?
- If yes → it’s a line of symmetry!
Tip: You can also use a mirror — place it on the line and see if the reflection looks the same as the hidden half.
Pick a line
Imagine folding
Match check
A shape can have 0, 1, 2, 4, or even infinite lines of symmetry — it depends on how regular the shape is.
Symmetry in letters
Letter symmetry depends on the font, but in simple block capitals:
- A, M, T, U, V, W, Y often have a vertical line of symmetry
- B, C, D, E can have a horizontal line of symmetry
- H, I, O, X often have both
Practice
How many lines of symmetry does a regular hexagon (6 equal sides) have?
A regular hexagon has 6 lines of symmetry — 3 connecting opposite corners and 3 connecting midpoints of opposite sides.
How many lines of symmetry does an equilateral triangle have?
An equilateral triangle has 3 lines of symmetry, one from each vertex to the midpoint of the opposite side.
Which of these shapes has NO lines of symmetry?
A parallelogram (that isn't a rectangle) has no lines of symmetry. You can't fold it so both halves match.
The letter H has how many lines of symmetry?
H has a vertical line of symmetry (left = right) and a horizontal one (top = bottom). That's 2.
A regular octagon (8 equal sides) has how many lines of symmetry?
A regular polygon with n sides always has n lines of symmetry. A regular octagon has 8.
Challenge
Quick-Fire Round