geometry · Year 4 · AC9M4SP03
Lines of symmetry
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.
Sample questions
How many lines of symmetry does a square have?
- A square maps exactly onto itself when it is folded along a line of symmetry.
- Folding a square every possible way, 4 folds match exactly.
- A square has 4 lines of symmetry.
Answer: 4
How many lines of symmetry does a rectangle have?
- A rectangle maps exactly onto itself when it is folded along a line of symmetry.
- Folding a rectangle every possible way, 2 folds match exactly.
- A rectangle has 2 lines of symmetry.
Answer: 2
How many lines of symmetry does a square have?
- A square maps exactly onto itself when it is folded along a line of symmetry.
- Folding a square every possible way, 4 folds match exactly.
- A square has 4 lines of symmetry.
Answer: 4