DfE statement G19 · Geometry and measures

Congruence and similarity: lengths, areas and volumes

part HigherEither paper

Congruence and similarity: lengths, areas and volumes is content statement G19 of the DfE GCSE mathematics subject content, in the geometry area. It is on both tiers, with a Higher-only part, and it appears on both the calculator and the non-calculator papers. 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 the concepts of congruence and similarity, including the relationships between lengths, areas and volumes in similar figures." (statement G19). 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 G19

Tier

Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "areas and volumes". Everything else in the statement is Foundation content.

Calculator

This turns up on both the non-calculator and the calculator papers, so practise it both ways — the written method for Paper 1 and the efficient calculator route for Papers 2 and 3.

Common mistakes

Scaling an area by the length scale factor rather than by its square.
Matching sides that do not correspond, because the two shapes are drawn in different orientations.
Assuming that two shapes with the same angles must be congruent. Equal angles make them similar; congruence needs equal sides too.

Sample questions (10 of 30)

G19 · Congruence and similarity: lengths, areas and volumesQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Geometry and measures

G19

Advanced

Triangle ABC and triangle DEF are similar. The area of triangle ABC is 36 cm² and the area of triangle DEF is 100 cm². Work out the ratio of the lengths of triangle ABC to the lengths of triangle DEF, in its simplest form.

💡 Hints:

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

Nearby statements

G1Geometric terms, notation and diagrams G2Ruler and compass constructions and loci G3Angle facts, parallel lines and polygons

Questions people ask

Is congruence and similarity: lengths, areas and volumes on Foundation or Higher?

Both, but not all of it. The parts the DfE prints in bold — "areas and volumes" — are Higher only; the rest is Foundation content.

Can I use a calculator for congruence and similarity: lengths, areas and volumes?

It depends on the paper. Paper 1 is non-calculator; Papers 2 and 3 allow one, and this topic is asked on both kinds.

What is the single most common mistake here?

Scaling an area by the length scale factor rather than by its square.

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.