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
In the diagram, $DE$ is parallel to $AB$ .

$AD = 9$ cm, $DC = 6$ cm, $DE = 4$ cm and $AB = 10$ cm.Diagram NOT accurately drawn

(a) Explain why triangle $CDE$ is similar to triangle $CAB$ .

(b) Work out the length of $CB$ , given that $CE = 5$ cm.
Level 4 · 5 marksTry it
2
Two bottles are mathematically similar. Their heights are $12$ cm and $18$ cm.

The smaller bottle holds $500$ ml.

Work out how much the larger bottle holds.
Level 4 · 3 marksTry it
3
Two mathematically similar rugs have areas $45$ m² and $125$ m².

The shorter side of the smaller rug is $6$ m.

Work out the shorter side of the larger rug.
Level 4 · 3 marksTry it
4
Two mathematically similar boxes have heights $10$ cm and $15$ cm.

The smaller box has volume $400$ cm³.

Work out the volume of the larger box.
Level 4 · 3 marksTry it
5
In triangle $ABC$ , the point $D$ lies on $AB$ and the point $E$ lies on $AC$ , with $DE$ parallel to $BC$ .

$AD = 4$ cm, $DB = 6$ cm and $DE = 6$ cm.Diagram NOT accurately drawn

Work out the length of $BC$ .
Level 4 · 3 marksTry it

7 more questions on similar shapes & missing lengths

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