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
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
2
Two similar tiles have corresponding sides of length $5$ cm and $8$ cm.

The smaller tile has an area of $40$ cm².

Work out the area of the larger tile.
Level 3 · 3 marksTry it
3
Two triangles are mathematically similar. A side of length $6$ cm in the smaller triangle corresponds to a side of length $9$ cm in the larger triangle.

(a) A second side of the smaller triangle is $8$ cm. Work out the corresponding side of the larger triangle.

(b) A side of the larger triangle is $15$ cm. Work out the corresponding side of the smaller triangle.
Level 3 · 3 marksTry it
4
The diagram shows a plan of a triangular courtyard, $ABC$ .Angle $ABC = 90°$

The plan is drawn to a scale of $1 : 200$

The area of the courtyard is $168$ m²

Work out the length of $BC$ on the plan.

(3 marks)
Level 3 · 3 marksTry it