This topic summary covers Knowledge Organiser: Properties of Quadrilaterals within Properties of Quadrilaterals for GCSE Mathematics. Revise Properties of Quadrilaterals in Geometry & Measures for GCSE Mathematics with 11 exam-style questions and 3 flashcards. This topic appears less often, but it can still be a useful differentiator on mixed-topic papers. It is section 9 of 10 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Properties of Quadrilaterals
Key Terms
- Parallelogram: Opposite sides parallel and equal
- Rhombus: 4 equal sides, opposite angles equal
- Trapezium: Exactly one pair of parallel sides
- Kite: Two pairs of adjacent equal sides
- Diagonal: Line joining opposite vertices
- Bisect: Cut exactly in half
Must-Know Facts
- All quadrilateral angles sum to 360°
- Square and rectangle: all angles = 90°
- Parallelogram: opposite angles equal; adjacent angles add to 180°
- Rhombus: 4 equal sides, diagonals bisect at 90°
- Kite: one pair of opposite angles equal; diagonals cross at 90°
- A square is a special rectangle AND a special rhombus
Key Methods
- Missing angle: sum of others + x = 360°
- Parallelogram adjacent angles: a + b = 180°
- Use shape properties to set up equations
- State the property used as your reason
Common Mistakes
- Confusing a rhombus and a square: Both have 4 equal sides, but a square also has 4 right angles — a rhombus does not unless it is also a square
- Assuming all parallelograms have right angles: Parallelogram opposite angles are equal and adjacent angles sum to 180°, but they are not 90° unless it is a rectangle
- Forgetting angles in a quadrilateral sum to 360°: This applies to all quadrilaterals — use it to find missing angles by subtracting the known three from 360°
- Mixing up diagonals: Diagonals bisect each other in parallelograms/rhombuses/rectangles, but only right-angle bisect in squares and rhombuses — check the specific shape
Practice questions for Properties of Quadrilaterals
Which of the following is a property of a parallelogram?
State THREE properties of a rhombus, at least one of which relates to its diagonals.
Quick recall flashcards
Rhombus
All sides equal, opposite angles equal
Parallelogram
Opposite sides parallel and equal