Properties of 2D shapes
Triangles
Sum of interior angles = 180°.
| Type | Property |
|---|---|
| Equilateral | All sides equal, all angles 60° |
| Isosceles | Two equal sides, two equal base angles |
| Scalene | All sides and angles different |
| Right-angled | One angle is 90° |
Exterior angle of a triangle = sum of the two opposite interior angles.
Quadrilaterals
Sum of interior angles = 360°.
| Shape | Sides | Angles | Diagonals |
|---|---|---|---|
| Square | 4 equal | 4 right angles | Equal, perpendicular, bisect |
| Rectangle | Opposite equal | 4 right angles | Equal, bisect |
| Parallelogram | Opposite equal & parallel | Opposite equal | Bisect each other |
| Rhombus | All equal | Opposite equal | Perpendicular bisectors |
| Kite | Two pairs adjacent equal | One pair opposite equal | Perpendicular |
| Trapezium | One pair parallel | — | — |
Polygons (n sides)
- Sum of interior angles = (n − 2) × 180°.
- Each interior angle of a regular polygon = (n − 2) × 180° / n.
- Each exterior angle of a regular polygon = 360° / n.
- Interior + exterior angle at each vertex = 180°.
Example: regular hexagon (n = 6). Exterior angle = 60°, interior angle = 120°.
CCEA reasoning marks
When a question says "give a reason", quote the geometric fact in standard wording: "angles in a triangle sum to 180°", "exterior angle of a regular pentagon = 360°/5", "opposite angles of a parallelogram are equal". A correct numerical answer without justification loses the B1 reasoning mark on Higher tier.
AI-generated · claude-opus-4-7 · v3-ccea-maths-leaves