Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Similarity — scale factors, similar triangles and area/volume ratios — to become a reliable source of marks instead of a topic they only half-remember.
What query it owns: how to understand and revise Similarity in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Similarity revision-guide angle, while Tutopiya’s Similarity subtopic page owns the learning resource and the free Similarity quiz owns the practice.

Similarity is one of the highest-value subtopics in the Geometry unit of Cambridge IGCSE Mathematics (0580/0607). When two shapes are similar, their corresponding sides are in the same ratio and their angles match — which lets you find missing lengths, areas and volumes from a single scale factor. This guide explains exactly what Similarity covers, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• Similar shapes have equal angles and sides in proportion — same shape, different size.
• The scale factor (k) links corresponding lengths: new length = k × original length.
• For area, multiply by k²; for volume, multiply by k³.
• In triangles, look for parallel lines or shared angles to prove similarity before calculating.

What is Similarity in Cambridge IGCSE Maths?

Similarity is the relationship between shapes that are the same shape but not necessarily the same size. In Cambridge IGCSE Mathematics, similar figures have matching angles and corresponding sides in a fixed ratio called the scale factor. You use similarity to find unknown lengths in triangles, compare areas of similar shapes, and solve problems involving enlargement and model scales.

You can read the full explanation, worked examples and notes on Tutopiya’s Similarity subtopic page before you attempt questions.

The core ideas you must master

These five ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Idea	What it means	How the exam uses it
Similar triangles	Equal angles; sides in proportion	”Triangle ABC is similar to triangle PQR”
Scale factor (length)	Ratio of corresponding sides	”The scale factor from ABC to PQR is 3”
Area ratio	Multiply area by k²	”The area of the larger triangle is…”
Volume ratio	Multiply volume by k³	”Two similar cones…”
Parallel lines	Often create similar triangles (AA)	Lines parallel to the base of a triangle

How to solve similarity problems — step by step

The most reliable method works for length, area and volume questions.

1. Confirm similarity — equal angles or given “similar” in the question.
2. Match corresponding sides — list sides that pair up (often by position or labelling order).
3. Find the scale factor k — k = (new side) ÷ (original side).
4. For a missing length, multiply or divide by k.
5. For area, use k²; for volume, use k³.
6. Sanity-check: the larger shape should have the larger k if you scaled up.

Once you have worked through a few, test yourself with the free Similarity quiz — it tells you fast whether the method has actually stuck.

Length vs area vs volume: which ratio does the question want?

Students lose marks by using k when the question asks about area or volume. Use the signal words to decide.

You want…	Formula	Typical signal words
Missing length	× or ÷ by k	”length”, “height”, “radius”
Area of similar shape	× or ÷ by k²	”area”, “surface area”
Volume of similar solid	× or ÷ by k³	”volume”, “capacity”, “similar cones/spheres”

Similarity in past-paper wording: command words that matter

Most lost marks in Similarity come from pairing the wrong sides or using k instead of k². These are the command words you will see and what each one demands.

Command word / phrase	What the question wants	Typical Similarity stem
Show that the triangles are similar	Prove equal angles (AA, SAS or SSS)	“Show that triangle ABC is similar to triangle ADE.”
Calculate / Work out	Find a length, area or volume	”Work out the length of PQ.”
Given that … are similar	Similarity is established — go straight to scale factor	”Given that the triangles are similar, find…”
Write down the scale factor	State k as a number or ratio	”Write down the scale factor of enlargement.”
Show that	Prove a given numerical result with working	”Show that the area of the larger triangle is 36 cm².”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just the ratios — is what method marks reward. Here is how three real-style stems are answered.

1. “Triangles ABC and DEF are similar. AB = 4 cm, DE = 10 cm, BC = 6 cm. Work out the length of EF.” Scale factor k = 10 ÷ 4 = 2.5. EF = 6 × 2.5 = 15 cm. Mark-scheme reward: correct k, then correct multiplication on corresponding sides.
2. “Two similar triangles have corresponding sides in the ratio 2 : 5. The area of the smaller triangle is 12 cm². Work out the area of the larger triangle.” Area ratio = k² = (5/2)² = 6.25. Area = 12 × 6.25 = 75 cm². Reward: using k², not k, for area.
3. “In triangle ABC, DE is parallel to BC. AD = 3 cm, DB = 2 cm, DE = 4.5 cm. Work out the length of BC.” Triangles ADE and ABC are similar (AA). k from small to large = (3+2)/3 = 5/3. BC = 4.5 × (5/3) = 7.5 cm. Reward: identifying similarity from parallel lines.

When you can recognise the wording instantly, work the full set on the Geometry topical past-paper questions and the Similarity quiz to lock the method in.

How Similarity connects to the rest of Geometry

Similarity builds on Pythagoras Theorem in right-angled triangle problems and links forward to Transformations, where enlargement uses a scale factor directly. Area and volume ratios also appear in mensuration questions across the syllabus. When you are ready to mix topics, the Cambridge IGCSE Maths resource hub lets you move straight from a weak subtopic into the next.

Common mistakes students make

• Pairing non-corresponding sides when finding the scale factor.
• Using k instead of k² for area or k³ for volume.
• Assuming triangles are similar without checking equal angles or given information.
• Inverting the scale factor (small ÷ large when the question wants large ÷ small).
• Forgetting that congruent shapes are similar with k = 1 — a special case, not a different topic.

When you need more support

If Similarity questions keep tripping you up — especially area and volume ratio problems — work through the Geometry topical past-paper questions and the Similarity quiz to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Is Similarity hard in Cambridge IGCSE Maths? It is medium difficulty. Length questions are straightforward once you identify corresponding sides; area and volume ratios catch students who forget k² and k³.

What is the easiest way to prove triangles are similar? Look for two equal angles (AA) — especially when a line is parallel to the base. Parallel lines often create matching corresponding angles.

What is the difference between similar and congruent? Congruent shapes are identical in size and shape (scale factor 1). Similar shapes have the same shape but can differ in size.

How do I revise Similarity effectively? Read the subtopic notes, practise labelling corresponding sides on every diagram, then take the Similarity quiz. Revisit any area-ratio questions you got wrong before moving on.

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