GCSE · Congruence & similarity

Similar shapes & missing lengthsExam-style questions

Why equal angles force sides into a fixed ratio, finding the scale factor the right way round, similar triangles hidden inside one figure, and the area and volume scale factors k² and k³.

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25 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 2 Level 3 Level 4 Level 5

1
Two rectangles are similar. The small one is $2$ cm by $3$ cm. The large one is $6$ cm wide. Work out the length of the large rectangle.
Level 1 · 2 marksTry it
2
Triangle $ABC$ has sides $3$ cm, $4$ cm and $5$ cm. Triangle $DEF$ is similar to $ABC$ and its shortest side is $6$ cm. Write down the scale factor of the enlargement from $ABC$ to $DEF$ .
Level 1 · 1 markTry it
3
Triangle $ABC$ has sides $3$ cm, $4$ cm and $5$ cm. Triangle $DEF$ is an enlargement of $ABC$ with scale factor $2$ . Write down the lengths of the three sides of $DEF$ .
Level 1 · 1 markTry it
4
Two triangles are similar. In the small triangle a side is $5$ cm; the matching side in the large triangle is $15$ cm. Another side of the small triangle is $4$ cm. Work out the matching side of the large triangle.
Level 2 · 2 marksTry it
5
Triangle $ABC$ and triangle $PQR$ are similar, with $AB$ corresponding to $PQ$ .Diagram NOT accurately drawn

(a) Work out the length of $QR$ .

(b) Work out the length of $AC$ .
Level 3 · 4 marksTry it

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