Topic summary · IGCSE handout

Similar Shapes 2 summary

Similarity scales lengths by $k$ , areas by $k^2$ , volumes by $k^3$ . Matching angles and proportional sides define similarity.

Open Learning Sheet — Similar Shapes 2 Download Similar Shapes 2 answers PDF

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Key learning points

Corresponding angles equal; corresponding sides in the same ratio.
Area factor $=(\text{length factor})^2$ ; volume factor cubed.
Find missing sides with matching vertices carefully labelled.

Worked example 1 — Area scale factor

Length SF $k=3$ . Area SF?

Working

9

Square $k$ .

Worked example 2 — Volume scale factor

Length SF $k=2$ . Volume SF?

Working

8

Cube $k$ .

Worked example 3 — Length from areas

Areas ratio $16:9$ . Length SF?

Working

4:3

Square-root of area SF.

Scaffolded Learning Sheet and answers (PDFs)

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Open Learning Sheet Answers PDF

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