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
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 10 of 10 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
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
Parallelogram
Opposite sides parallel and equal
Rhombus
All sides equal, opposite angles equal