Quadrilaterals (Edexcel GCSE Maths): Revision Notes
Quadrilaterals
What is a quadrilateral?
A quadrilateral is any shape that has exactly four sides. When you draw lines connecting opposite corners of a quadrilateral, these lines are called diagonals.
Types of quadrilaterals and their properties
Understanding the different types of quadrilaterals and their unique properties is essential for GCSE geometry. Each type has specific characteristics that make it distinct from the others.
Square
A square is a special type of quadrilateral where all sides and angles are equal.
Key properties:
- All four sides are equal in length
- All four angles are 90°
- Diagonals are equal in length and bisect each other at 90°
- Has 4 lines of symmetry
- Has rotational symmetry of order 4
Bisect means 'cut in half exactly'. This is a key term that appears frequently in geometry questions.
Rectangle
A rectangle is a quadrilateral with opposite sides equal and all angles at 90°.
Key properties:
- Opposite sides are equal in length
- All four angles are 90°
- Diagonals are equal in length and bisect each other
- Has 2 lines of symmetry
- Has rotational symmetry of order 2
Parallelogram
A parallelogram is a quadrilateral where opposite sides are parallel and equal.
Key properties:
- Opposite sides are parallel and equal in length
- Opposite angles are equal
- Diagonals bisect each other but are not equal in length
- Has no lines of symmetry
- Has rotational symmetry of order 2
Matching arrows in diagrams show which lines are parallel, and matching dashes show which lines are the same length. This notation is crucial for identifying properties in exam questions.
Trapezium
A trapezium is a quadrilateral with exactly one pair of parallel sides.
Key properties:
- One pair of opposite sides are parallel
- The parallel sides are called bases
- No other special properties guaranteed
A trapezium only requires exactly one pair of parallel sides. If both pairs of opposite sides are parallel, it becomes a parallelogram instead.
Kite
A kite is a quadrilateral with two pairs of adjacent sides that are equal.
Key properties:
- Two pairs of adjacent sides are equal in length
- One pair of opposite angles are equal
- Diagonals cross at 90° to each other
- Has 1 line of symmetry
Rhombus
A rhombus is a quadrilateral where all four sides are equal in length.
Key properties:
- All four sides are equal in length
- Opposite sides are parallel
- Opposite angles are equal
- Has 2 lines of symmetry
- Diagonals bisect each other at 90°
- Has rotational symmetry of order 2
Common Mistake to Avoid: Don't confuse a rhombus with a square. A rhombus has all sides equal but angles are not necessarily 90°. A square is a special case of a rhombus where all angles are also 90°.
Exam tips
Essential Exam Strategy:
- Learn to recognise quadrilaterals by their properties, not just their appearance
- Use the notation symbols: arrows for parallel lines, dashes for equal lengths
- Remember that squares and rectangles are special types of parallelograms
- A rhombus is a parallelogram with all sides equal
- Always check how many lines of symmetry each quadrilateral has
Key Points to Remember:
- A quadrilateral is any four-sided shape with diagonals connecting opposite corners
- Each type of quadrilateral has unique combinations of equal sides, equal angles, and symmetry properties
- Squares have the most special properties (all sides equal, all angles 90°, 4 lines of symmetry)
- Trapeziums only require one pair of parallel sides
- Understanding these properties helps you identify and classify quadrilaterals correctly in exams