Fold paper shapes in half. Do the two halves match? If yes, that fold is a line of symmetry.
Build a polygon
regular hexagon
interior each
120.0°
120.0°
exterior each
60.0°
60.0°
interior sum
720°
720°
diagonals
9
9
The fold test
A line of symmetry is any fold where the two halves land exactly on top of each other. A square folds four ways (two diagonals, plus horizontal and vertical); a plain rectangle only two; a circle infinitely many.
A regular polygon with n sides has exactly n lines of symmetry. Triangle → 3, pentagon → 5, octagon → 8. Stretch or skew it and most of those lines vanish.
Your turn
How many lines of symmetry does a regular hexagon have, and how many does a (non-square) rectangle have?
Lines of symmetry
- Square — 4 (two diagonals + horizontal + vertical)
- Rectangle — 2 (horizontal + vertical)
- Equilateral triangle — 3
- Circle — infinite
- Scalene triangle — 0
Regular polygons of n sides always have exactly n lines of symmetry. Asymmetric shapes have zero.