Properties of 2D Shapes
Identifying and describing triangles, quadrilaterals, polygons and circles and their properties.
What is Properties of 2D Shapes?
In the 11+ exam, you need to know the names and properties of common 2D shapes, including the number of sides, angles, lines of symmetry, and whether sides are equal or parallel.
Key shape families include triangles (equilateral, isosceles, scalene, right-angled), quadrilaterals (square, rectangle, parallelogram, rhombus, trapezium, kite), and regular polygons.
Step-by-Step Method
Count the sides
Triangle = 3, quadrilateral = 4, pentagon = 5, hexagon = 6, heptagon = 7, octagon = 8.
Check for equal sides
Are all sides equal (regular)? Are some sides equal? Mark equal sides on your diagram.
Check for parallel sides
Parallel sides are marked with arrows. A parallelogram has 2 pairs, a trapezium has 1 pair.
Check the angles
Are there right angles? Are any angles equal? Use the angle sum rules to check.
Count lines of symmetry
A line of symmetry divides the shape into two identical halves. Fold the shape mentally along the line.
Worked Examples
A shape has 4 sides, all sides equal, and no right angles. What is it?
Working
- 4 sides = quadrilateral.
- All sides equal = could be square or rhombus.
- No right angles = not a square.
How many lines of symmetry does a regular hexagon have?
Working
- A regular hexagon has 6 equal sides and 6 equal angles.
- Regular polygons have the same number of lines of symmetry as they have sides.
Name the quadrilateral with exactly one pair of parallel sides.
Working
- Square: 2 pairs. Rectangle: 2 pairs. Parallelogram: 2 pairs. Rhombus: 2 pairs.
- Kite: 0 pairs.
- Trapezium: exactly 1 pair.
Common Mistakes
Forgetting that a square is also a rectangle, a rhombus and a parallelogram.
A square is a special case of all three. It has all their properties plus right angles and equal sides.
Confusing a rhombus with a diamond shape that is not a quadrilateral.
A rhombus is a quadrilateral with 4 equal sides. Think of it as a “squashed square”.
Thinking regular means “has right angles”.
Regular means all sides equal AND all angles equal. A regular pentagon has no right angles.
Top Tips
- Learn the triangle types: equilateral (all equal), isosceles (two equal), scalene (none equal), right-angled (one 90-degree angle).
- A regular polygon with n sides has n lines of symmetry and rotational symmetry of order n.
- Parallel lines are marked with arrows on diagrams. Equal sides are marked with small dashes.
- Remember the quadrilateral hierarchy: square is a special rectangle, which is a special parallelogram.
Ready to practise?
Put these techniques into action with our free practice papers.
Practise Maths Questions