A line of symmetry is a fold line that makes the two halves of a shape land exactly on top of each other. To count them, imagine folding the shape every possible way and keep only the folds where the halves match. A rectangle has 2 lines (side to side and top to bottom) — its diagonals do NOT work. A square has 4, because it can also fold corner to corner. A parallelogram has none, because its slant tips one half off the other. Looking balanced is not the same as being symmetrical: only the fold test decides.
Explore this idea with maths tools
Maths you can move
Build 8 + 5
Tap two gold counters to fill the ten-frame.
8 in the frame + 5 waiting. The total stays the same.
Words to know
- line of symmetry
- a fold line where the two halves match exactly
- diagonal
- a line joining opposite corners
Worked examples
How many lines of symmetry does a rectangle have?
- 1.Fold side to side and top to bottom — both match.
- 2.The diagonals do not match, so there are 2.
= 2
How many lines of symmetry does a square have?
- 1.Fold side to side, top to bottom, and both diagonals.
- 2.All 4 folds match, so there are 4.
= 4
How many lines of symmetry does an equilateral triangle have?
- 1.Fold from each corner to the middle of the opposite side.
- 2.Three folds match, so there are 3.
= 3
For parents
Method: Cut the shape out of paper and fold it every way.
What to say: Ask 'do the two halves land exactly on top of each other?' for each fold.
Common mistakes:
- Drawing a rectangle's diagonals as symmetry lines (saying 4 instead of 2).
- Forgetting a square's two diagonal folds (saying 2 instead of 4).