Sheet № 208 · Foundation + Higher · AQA · Edexcel · OCR
Properties of Quadrilaterals –
Properties of quadrilaterals is a key GCSE Maths topic that appears on Foundation and Higher papers across AQA, Edexcel, and OCR. You need to know the defining features of each quadrilateral — side lengths, angle sizes, diagonal properties, and lines of symmetry — so you can identify shapes, justify geometric proofs, and solve angle probl
§Key definitions
Question:
A parallelogram has one angle of 65°. Find the other three angles.
Answer:
The four angles are 65°, 115°, 65°, and 115°.
Q1 (Foundation):
A rectangle has a diagonal of 13 cm and a width of 5 cm. Find the length of the rectangle.
Q2 (Foundation):
An isosceles trapezium has angles of 72° and 72° at the base. Find the other two angles.
Q3 (Higher):
A rhombus has an angle of 50°. The shorter diagonal is 8 cm. Find the length of the longer diagonal to 1 d.p.
§Formulas to memorise
Apply any known equal-angle rules (e.g. opposite angles in a parallelogram are equal).
Worked example
A parallelogram has one angle of 65°. Find the other three angles.
Working:
⚠ Common mistakes
- ✗Confusing a rhombus with a square. A rhombus has four equal sides but does not require right angles. A square is a special rhombus with 90° angles.
- ✗Forgetting that a square is also a rectangle (and a parallelogram). Properties are inherited — every property of a rectangle also applies to a square.
- ✗Assuming trapeziums have equal diagonals. Only an isosceles trapezium has equal diagonals; a general trapezium does not.
✦ Exam tips
- →Draw and label a quick sketch if the question does not provide a diagram. Mark equal sides with tick marks and right angles with small squares.
- →When asked to "explain why" a shape is a specific quadrilateral, state at least two defining properties (e.g. "all sides equal and no right angles, so it is a rhombus").
- →Remember that the angle sum of 360° applies to every quadrilateral and is often the starting point for angle calculations.