Knowing the properties of common 2D shapes — sides, angles, symmetry — is essential for identifying shapes, solving geometry problems, and writing proofs.
Triangles:
- Equilateral: 3 equal sides, 3 equal angles (60°), 3 lines of symmetry
- Isosceles: 2 equal sides, 2 equal base angles, 1 line of symmetry
- Scalene: no equal sides, no equal angles, no symmetry
- Right-angled: one 90° angle
Quadrilaterals:
- Square: 4 equal sides, 4 right angles, 4 lines of symmetry, rotational order 4
- Rectangle: opposite sides equal, 4 right angles, 2 lines of symmetry
- Rhombus: 4 equal sides, opposite angles equal, diagonals bisect at 90°, 2 lines of symmetry
- Parallelogram: opposite sides parallel and equal, opposite angles equal, no lines of symmetry
- Trapezium: one pair of parallel sides
- Kite: 2 pairs of adjacent equal sides, one diagonal is a line of symmetry, diagonals meet at 90°
Regular polygons: all sides equal, all angles equal. Interior angle $= \frac{(n-2) \times 180°}{n}$.
Common error: confusing rhombus and square — a rhombus has equal sides but its angles are not necessarily 90°.