Properties of 2D ShapesEdexcel GCSE Maths: Revision notes
Section 1
Naming Points, Lines and Polygons
Geometry uses precise vocabulary that you must use correctly in explanations:
- Points, lines, vertices (corners) and edges (sides) are the basic building blocks of shapes
- Parallel lines never meet and stay the same distance apart; perpendicular lines meet at a right angle (90°)
- A polygon is any closed 2D shape made of straight sides
Using this vocabulary correctly is essential when describing or proving properties of shapes.
Section 2
Properties of Triangles, Quadrilaterals and Polygons
Every polygon can be described by its number of sides, its angles, its diagonals and its symmetry:
| Shape | Number of sides |
|---|---|
| Triangle | 3 |
| Quadrilateral | 4 |
| Pentagon | 5 |
| Hexagon | 6 |
| Octagon | 8 |
A regular polygon has all sides and all angles equal; an irregular polygon does not. A diagonal is a line segment joining two non-adjacent vertices.
Section 3
The Special Quadrilaterals
Each special quadrilateral has its own set of properties:
| Shape | Key properties |
|---|---|
| Square | 4 equal sides, 4 right angles, both pairs of sides parallel |
| Rectangle | Opposite sides equal, 4 right angles, both pairs of sides parallel |
| Parallelogram | Opposite sides equal and parallel, opposite angles equal |
| Trapezium | Exactly one pair of parallel sides |
| Kite | Two pairs of adjacent equal sides, one pair of opposite equal angles |
| Rhombus | 4 equal sides, opposite sides parallel, opposite angles equal |
Knowing these properties lets you identify a shape from a description, or use its properties to find missing angles and lengths.
A square is a special rectangle AND a special rhombus — don't treat these categories as mutually exclusive.
Section 4
Symmetry of 2D Shapes
A shape has a line of symmetry if it can be folded along that line so both halves match exactly. A shape has rotational symmetry of order n if it looks identical after being rotated by (360/n)° about its centre, for n rotations in a full turn.
Example: a square has 4 lines of symmetry and rotational symmetry of order 4. An equilateral triangle has 3 lines of symmetry and rotational symmetry of order 3.
Section 5
Angle Sums in Polygons
The interior angles of any polygon follow fixed rules:
- Sum of interior angles of a triangle = 180°
- Sum of interior angles of any polygon with n sides = (n − 2) × 180°
- For a regular polygon, each interior angle = (n − 2) × 180° ÷ n
- Each exterior angle of a regular polygon = 360° ÷ n
- Interior angle + exterior angle = 180° (they are on a straight line)
A regular hexagon (n = 6): sum of interior angles = (6 − 2) × 180 = 720°; each interior angle = 720 ÷ 6 = 120°; each exterior angle = 360 ÷ 6 = 60°.
Must Know
- A polygon's properties are described by its number of sides, angles, diagonals and symmetry
- Learn the specific properties of square, rectangle, parallelogram, trapezium, kite and rhombus — a square is both a special rectangle and a special rhombus
- Line of symmetry: shape folds onto itself exactly; order of rotational symmetry: number of matches in one full turn
- Sum of interior angles of a polygon = (n − 2) × 180°
- Each interior angle of a regular polygon = (n − 2) × 180° ÷ n; each exterior angle = 360° ÷ n
- Interior angle + exterior angle = 180°
That's the notes covered.
Carry on to the next subtopic.