Symmetry (Copy)
Cheat Sheet: Line Symmetry and Rotational Symmetry (IGCSE Mathematics 0580 – CORE)
Topic: Symmetries of Triangles, Quadrilaterals, and Polygons
1. Line Symmetry (Mirror Symmetry)
- A shape has line symmetry if it can be folded along a line so that both halves match exactly.
- The line is called the line of symmetry.
2. Rotational Symmetry
- A shape has rotational symmetry if it looks the same after being rotated (turned) around a point by less than 360°.
- The number of times it matches its original position in one full turn (360°) is called its order of rotational symmetry.
3. Symmetries of Common Shapes
| Shape | Number of Lines of Symmetry | Order of Rotational Symmetry |
|---|---|---|
| Equilateral Triangle | 3 | 3 |
| Isosceles Triangle | 1 | 1 |
| Scalene Triangle | 0 | 1 |
| Square | 4 | 4 |
| Rectangle | 2 | 2 |
| Rhombus | 2 | 2 |
| Parallelogram | 0 | 2 |
| Kite | 1 | 1 |
| Trapezium (regular) | 1 | 1 |
| Regular Pentagon | 5 | 5 |
| Regular Hexagon | 6 | 6 |
| Regular Octagon | 8 | 8 |
| Regular Decagon | 10 | 10 |
4. Key Properties
- Equilateral Triangle: All sides and angles are equal.
- Isosceles Triangle: Two sides and two angles are equal.
- Scalene Triangle: No sides or angles are equal.
- Square: All sides equal, all angles 90°.
- Rectangle: Opposite sides equal, all angles 90°.
- Rhombus: All sides equal, opposite angles equal.
- Parallelogram: Opposite sides parallel and equal, opposite angles equal.
- Kite: Two pairs of adjacent sides equal.
5. Important Tips
- Regular polygons (all sides and angles equal) have as many lines of symmetry and rotational order as they have sides.
- Irregular shapes often have fewer or no symmetries.
- A shape with only rotational symmetry but no line symmetry (like a parallelogram) still has rotational order greater than 1.
This covers CORE-level facts for recognising and interpreting line symmetry and rotational symmetry for triangles, quadrilaterals, and polygons.