Knowing the properties of 2D shapes — their sides, angles, diagonals, and symmetry — is fundamental to GCSE Geometry.
Triangles
| Type | Sides | Angles |
|---|---|---|
| Equilateral | All equal | All 60° |
| Isosceles | Two equal | Two equal |
| Scalene | All different | All different |
| Right-angled | — | One 90° angle |
Angle sum: .
Quadrilaterals
| Shape | Properties |
|---|---|
| Square | 4 equal sides, 4 right angles, 4 lines of symmetry |
| Rectangle | Opposite sides equal, 4 right angles, 2 lines of symmetry |
| Parallelogram | Opposite sides equal and parallel, opposite angles equal |
| Rhombus | 4 equal sides, opposite angles equal, diagonals bisect at 90° |
| Trapezium | One pair of parallel sides |
| Kite | Two pairs of adjacent equal sides, one pair of equal angles |
Angle sum: .
Regular Polygons
Interior angle of a regular -gon: .
Exterior angle: .
| Polygon | Sides | Interior Angle |
|---|---|---|
| Pentagon | 5 | 108° |
| Hexagon | 6 | 120° |
| Octagon | 8 | 135° |
Practice Problems
- Name a quadrilateral with 4 equal sides but no right angles.
- Find the interior angle of a regular decagon (10 sides).
- The exterior angle of a regular polygon is 40°. How many sides?
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Key Takeaways
Triangle angle sum = 180°. Quadrilateral = 360°.
Interior angle of regular polygon = .
Exterior angles of any polygon sum to 360°.