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DfE statement G4 · Geometry and measures

Properties of triangles and quadrilaterals

Both tiersNon-calculator

Properties of triangles and quadrilaterals is content statement G4 of the DfE GCSE mathematics subject content, in the geometry area. It is on both tiers, and it is examined without a calculator. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Derive and apply the properties and definitions of: special types of quadrilaterals, including square, rectangle, parallelogram, trapezium, kite and rhombus; and triangles and other plane figures using appropriate language." (statement G4). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.

— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement G4

Tier

Both tiers. This statement is Foundation content, which means Higher students are examined on it too — Higher is Foundation plus more, never instead of it.

Calculator

This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.

Common mistakes

  • Assuming a trapezium is isosceles, and so that its base angles are equal, when nothing says it is.
  • Giving a parallelogram lines of symmetry. It has rotational symmetry of order 2 and no line of symmetry unless it is also a rectangle or a rhombus.
  • Assuming the diagonals of a kite bisect each other. Only one of them bisects the other, and they cross at right angles.

Sample questions (10 of 30)

G4 · Properties of triangles and quadrilateralsQuestion 1 of 10 · 0 correct
Practice mode· no pressure · hints available

Geometry and measures

G4

Intermediate

In a kite, one pair of opposite angles are equal in size. In kite WXYZ, angle X = 40° and angle Z = 100° are the two angles that are NOT equal to each other. The other two angles, W and Y, are equal to each other. Work out the size of angle W.

💡 Hints:
Foundation worksheetHigher worksheetFoundation geometry and measures practiceHigher geometry and measures practice

Nearby statements

G2Ruler and compass constructions and lociG3Angle facts, parallel lines and polygonsG5Congruence criteria for trianglesG6Geometric reasoning and simple proofs

Questions people ask

Is properties of triangles and quadrilaterals on Foundation or Higher?

Both. It is Foundation content, so it can be asked on either tier.

Can I use a calculator for properties of triangles and quadrilaterals?

Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.

What is the single most common mistake here?

Assuming a trapezium is isosceles, and so that its base angles are equal, when nothing says it is.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

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