Properties of Quadrilaterals

In a Nutshell

Quadrilaterals are four-sided shapes. Each type (square, rectangle, parallelogram, rhombus, trapezium, kite) has its own combination of equal sides, parallel sides and equal angles.

Every quadrilateral has four sides and four angles that sum to 360°360°. The special quadrilaterals differ in their symmetry and which sides or angles are equal.

  • Square: 4 equal sides, 4 right angles, 2 pairs of parallel sides, 4 lines of symmetry.
  • Rectangle: opposite sides equal, 4 right angles, 2 pairs of parallel sides, 2 lines of symmetry.
  • Parallelogram: opposite sides equal and parallel, opposite angles equal, no lines of symmetry.
  • Rhombus: 4 equal sides, opposite angles equal, 2 pairs of parallel sides, 2 lines of symmetry.
  • Trapezium: exactly 1 pair of parallel sides.
  • Kite: 2 pairs of adjacent sides equal, 1 pair of opposite angles equal, 1 line of symmetry.

A square is a special rectangle (all sides equal) and a special rhombus (all angles 90°90°). A rectangle and rhombus are both special parallelograms.

Shape property explorer An interactive diagram that shows different shapes and highlights their key properties such as equal sides, parallel sides, and angles.

Select each quadrilateral to see its shape and properties. Tick marks show equal sides; arrows show parallel sides; small squares show right angles.

Watch it work

Question: A shape has four sides. Opposite sides are equal and parallel, but the angles are not 90°90°. What is the shape?

Have a go

Q1. Name a quadrilateral with exactly one pair of parallel sides.

Q2. True or false: every square is a rectangle.

Q3. How many lines of symmetry does a parallelogram have?

Q4. A kite has angles 80°,120°,80°80°, 120°, 80° and xx. Find xx.

Q5. A shape has 4 equal sides and 2 lines of symmetry but its angles are not right angles. Name the shape.