Learn the Test
1Imagine the fold.
A line of symmetry folds the shape so the two halves match exactly.
2Test every candidate.
Try vertical, horizontal AND diagonal lines — some work, some don't.
3Use the regular shortcut.
A regular polygon has as many lines of symmetry as sides: pentagon 5, hexagon 6.
Worked Example
How many lines of symmetry?
Watch Out! Common Mistakes
The classic! Fold a rectangle along a diagonal — the halves don’t match. It has only 2 lines.
Wrong! A general parallelogram has 0 lines of symmetry (it has rotational symmetry instead).
Count all four! A square’s lines: vertical, horizontal AND both diagonals.
⬇ Cheat Sheet
- Line of symmetry = fold line where halves match exactly.
- Test vertical, horizontal and diagonal candidates.
- Regular polygon: lines = sides.
- Rectangle 2 · square 4 · parallelogram 0 · circle infinite.
📖 Continue Your Journey
Quick summary
- A line of symmetry folds a shape onto itself exactly.
- Rectangle: 2 lines — its diagonals are NOT lines of symmetry.
- Regular polygons have as many lines as sides; circles have infinitely many.
- A general parallelogram has no lines of symmetry at all.
Frequently asked questions
Why aren't a rectangle's diagonals lines of symmetry?
Fold along a diagonal and the two halves overhang instead of matching — only the vertical and horizontal centre lines work, giving 2 lines.
How many lines of symmetry does a regular polygon have?
The same as its number of sides: equilateral triangle 3, square 4, regular pentagon 5, and so on.
Which common shape has no lines of symmetry?
A general parallelogram — a surprise to most children, since it looks so balanced. Its symmetry is rotational, not reflective.
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