Lines of Symmetry
A line of symmetry is a fold that lands one half exactly on the other. Turn the mirror and see how rarely that happens. Most lines miss.
A line of symmetry
Fold along this line and the two halves land exactly on each other — the reflection has come down on the shape.
- The shape
- Rectangle
- Lines of symmetry
- 2
Drag the end of the mirror line to turn it.
The shape
Ready to try some? Lines of symmetry worksheets
Where it usually goes wrong
Symmetry gets assumed. Asked how many lines a parallelogram has, most people say two and point at the diagonals — the diagonals cut it into equal halves, which is a different thing from a fold that lands one half on the other. Fold a parallelogram along its diagonal and the halves do not land. It has no lines of symmetry at all.
Try this
- Choose the parallelogram and turn the mirror all the way around. Nothing lands, including both diagonals.
- Choose the rectangle. Two lines work and the diagonals still do not — the same test, a different shape.
- Choose the hexagon and press Show every line. Six, which is more than most people guess.
Where this goes next
Symmetry is the first property of a shape that survives moving it, which is the idea Slide, Turn, Flip is built on and the reason it matters later.
More about angles and shapes
- Translations, Rotations and Reflectionsa move changes where a shape is, not what it is
- Angle Pairs That Add to 180°two angles at a point move in opposite directions while their total refuses to change
- Compass and Straightedge Constructionswhy a compass construction works whatever the compass is opened to