DfE statement G6 · Geometry and measures

Geometric reasoning and simple proofs

Both tiersNon-calculator

Geometric reasoning and simple proofs is content statement G6 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: "Apply angle facts, triangle congruence, similarity and properties of quadrilaterals to conjecture and derive results about angles and sides, including Pythagoras’ Theorem and the fact that the base angles of an isosceles triangle are equal, and use known results to obtain simple proofs." (statement G6). 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 G6

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

Stating a correct fact with no reason attached. In a reasoning question, the reason is the mark.
Assuming from the diagram that a triangle is isosceles or that two lines are parallel when the question has not said so.
Using the result you are trying to prove as one of the steps in the proof.

Formulae for this statement

Pythagoras' theorema² + b² = c²You must know this

Sample questions (10 of 30)

G6 · Geometric reasoning and simple proofsQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Geometry and measures

Intermediate

A rectangular gate is braced with a diagonal strut. The gate is 1.2 m wide and 0.9 m tall. Work out the exact length of the diagonal strut.

💡 Hints:

Foundation worksheet Higher worksheet Foundation geometry and measures practice Higher geometry and measures practice

Nearby statements

G4Properties of triangles and quadrilaterals G5Congruence criteria for triangles G7Transformations: rotation, reflection, translation, enlargementpart Higher G8Combinations of transformations and invarianceHigher only

Questions people ask

Is geometric reasoning and simple proofs on Foundation or Higher?

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

Can I use a calculator for geometric reasoning and simple proofs?

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?

Stating a correct fact with no reason attached. In a reasoning question, the reason is the mark.

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.

Back to Geometry and measures at Foundation or at Higher.