DfE statement G5 · Geometry and measures

Congruence criteria for triangles

Both tiersNon-calculator

Congruence criteria for triangles is content statement G5 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: "Use the basic congruence criteria for triangles (SSS, SAS, ASA, RHS)." (statement G5). 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 G5

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

Using SSA as a congruence criterion. Two sides and a non-included angle do not fix a triangle.
Quoting AAA. Equal angles give similarity, not congruence, because the triangles can be different sizes.
Showing the sides and angles match but never naming the criterion, which is the mark the question is actually testing.

Sample questions (10 of 30)

G5 · Congruence criteria for trianglesQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Geometry and measures

Intermediate

Triangle ABC has AB = 5 cm and BC = 7 cm. Triangle DEF has DE = 5 cm and EF = 7 cm. Which extra fact would prove the triangles are congruent by SAS?

💡 Hints:

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

Nearby statements

G3Angle facts, parallel lines and polygons G4Properties of triangles and quadrilaterals G6Geometric reasoning and simple proofs G7Transformations: rotation, reflection, translation, enlargementpart Higher

Questions people ask

Is congruence criteria for triangles on Foundation or Higher?

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

Can I use a calculator for congruence criteria for triangles?

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?

Using SSA as a congruence criterion. Two sides and a non-included angle do not fix a triangle.

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.