Learning pack · IGCSE handout

Pythagoras

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Pythagoras’ theorem links the three sides of a right-angled triangle: $a^2+b^2=c^2$ with $c$ the hypotenuse.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: 16_pythagoras_handout.pdf · 16_pythagoras_handout_answers.pdf

Full topic summary

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

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).

🎬 Topic videos

Pythagoras' Theorem (3 of 3: Summary)
Eddie Woo · 8 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Introduction to Pythagoras' Theorem
Eddie Woo · 15 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Proof of Pythagoras' Theorem (Redux)
Eddie Woo · 15 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Pythagoras | CIE IGCSE Foundation Maths (Lower Secondary)
IMProjectLessons · 8 min
IMProject original: Pythagoras self-study lesson for Lower Secondary / CIE Foundation. Pairs with Foundation handout + slides. Boards LowerSecondary + CIE; syllabus LS + 0580 Core / 0607 Core.
Pythagoras' Theorem (introduction)
Eddie Woo · 6 min
Clear classroom intro to Pythagoras. Use when starting right-angled triangles.
Visual Proof of Pythagoras' Theorem
Eddie Woo · 11 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.

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Browse the hub Learning Packs & Summary, or open the compact Pythagoras summary.