Symmetry
4.5 Symmetry – Cheat Sheet
1. Line Symmetry in 2D Shapes
- A line of symmetry divides a shape into two mirror-image halves.
- Also called mirror line.
- Number of lines of symmetry depends on shape type.
| Shape | Lines of Symmetry |
|---|---|
| Equilateral triangle | 3 |
| Isosceles triangle | 1 |
| Square | 4 |
| Rectangle | 2 |
| Circle | Infinite |
| Regular hexagon | 6 |
2. Rotational Symmetry in 2D Shapes
- A shape has rotational symmetry if it can be rotated less than 360° and still look the same.
- Order of rotational symmetry = number of times the shape matches itself in one full rotation.
| Shape | Order of Rotational Symmetry |
|---|---|
| Square | 4 |
| Rectangle | 2 |
| Equilateral triangle | 3 |
| Circle | Infinite |
| Regular pentagon | 5 |
3. Symmetry Properties of 3D Shapes
| Solid | Symmetry Features |
|---|---|
| Prism | Same cross-section along length, planes of symmetry through centre, rotational symmetry along axis |
| Cylinder | Infinite lines of symmetry around curved surface, 2 planes of symmetry through axis, rotational symmetry of any angle around central axis |
| Pyramid (square base) | 4 planes of symmetry through apex and base edges |
| Cone | Infinite lines of symmetry through axis, rotational symmetry around axis |
4. Symmetry Properties of Polygons
- Regular polygons:
- Number of lines of symmetry = number of sides
- Order of rotational symmetry = number of sides
- Irregular polygons:
- Symmetry depends on side and angle equality
- Often fewer or no lines of symmetry
5. Symmetry in Triangles
| Triangle Type | Lines of Symmetry | Rotational Symmetry Order |
|---|---|---|
| Equilateral | 3 | 3 |
| Isosceles | 1 | 1 |
| Scalene | 0 | 1 |
| Right-angled isosceles | 1 | 1 |
6. Symmetry in Quadrilaterals
| Quadrilateral | Lines of Symmetry | Rotational Symmetry Order |
|---|---|---|
| Square | 4 | 4 |
| Rectangle | 2 | 2 |
| Rhombus | 2 | 2 |
| Parallelogram | 0 | 2 |
| Kite | 1 | 1 |
| Trapezium (isosceles) | 1 | 1 |