Properties of Quadrilaterals
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 . 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 ). A rectangle and rhombus are both special parallelograms.
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 . What is the shape?
Step 1: Opposite sides equal and parallel tells us it is at least a parallelogram.
Step 2: No right angles rules out a rectangle or square. We need to know if all four sides are equal.
Answer: If all four sides are equal, it is a rhombus. If only opposite pairs are equal, it is a parallelogram.
Have a go
Q1. Name a quadrilateral with exactly one pair of parallel sides.
Trapezium.
Q2. True or false: every square is a rectangle.
True. A square has opposite sides equal and all angles , so it meets the definition of a rectangle.
Q3. How many lines of symmetry does a parallelogram have?
Zero (unless it is also a rectangle or rhombus).
Q4. A kite has angles and . Find .
, so .
.
Q5. A shape has 4 equal sides and 2 lines of symmetry but its angles are not right angles. Name the shape.
Rhombus.