Topic summary · IGCSE handout

Pythagoras summary

Pythagoras’ theorem links the three sides of a right-angled triangle: $a^2+b^2=c^2$ with $c$ the hypotenuse.

Open Learning Sheet — Pythagoras Download Pythagoras answers PDF

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Key learning points

Only for right-angled triangles; identify the hypotenuse first (opposite the right angle).
To find a shorter side: subtract squares, then square-root.
Leave answers in surd form when exact values are required.

Worked example 1 — Find the hypotenuse

Legs $6$ and $8$ . Find the hypotenuse.

Working

c=\sqrt{6^2+8^2}=10

Multiple of 3-4-5.

Worked example 2 — Find a shorter side

Hypotenuse $13$ , leg $5$ . Other leg?

Working

b=\sqrt{13^2-5^2}=12

Subtract squares, then square-root.

Worked example 3 — Converse

Sides $7$ , $24$ , $25$ . Right-angled?

Working

7^2+24^2=25^2\Rightarrow\text{yes}

Converse of Pythagoras.

Worked example 4 — 3D edge

Cuboid $3\times4\times12$ . Space diagonal?

Working

\sqrt{3^2+4^2+12^2}=13

Apply Pythagoras twice (or once in 3D).

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.

Open Learning Sheet Answers PDF

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