Symmetry
4 minQuiz at the end
Line (Reflection) Symmetry
A shape has line symmetry if it can be folded so that one half fits exactly on the other. The fold line is the line of symmetry (or mirror line).
| Shape | Lines of symmetry |
|---|---|
| Equilateral triangle | 3 |
| Square | 4 |
| Rectangle | 2 |
| Regular hexagon | 6 |
| Circle | Infinite |
| Scalene triangle | 0 |
Rotational Symmetry
A shape has rotational symmetry if it looks identical after a rotation of less than 360Β°.
The order of rotational symmetry is how many times the shape looks the same in one full turn.
| Shape | Order |
|---|---|
| Square | 4 |
| Equilateral triangle | 3 |
| Rectangle | 2 |
| Regular hexagon | 6 |
| Scalene triangle | 1 (no rotational symmetry) |
Order 1 means the shape only looks the same after a complete 360Β° turn β effectively no rotational symmetry.
Symmetry in Coordinates
If a shape is symmetric about the y-axis, for every point (x, y) there is a corresponding (-x, y).
Using Symmetry
Symmetry helps solve problems by reducing the number of angles or lengths you need to calculate β a property shared by symmetric parts.