Grade 10 · Geometry · 74 pages · PDF

Pythagoras’ Theorem

Clear, exam-focused notes on Pythagoras’ theorem, from finding missing sides to 3D problems, with diagrams and fully worked examples.

A complete 20-page IGCSE guide to Pythagoras’ theorem. It starts with right-angled triangles and identifying the hypotenuse. It then teaches how to find the hypotenuse, how to find a shorter side, and how to use the converse to test whether a triangle is right-angled. It also covers Pythagorean triples and their multiples. Later sections apply the theorem to isosceles and equilateral triangles, rectangle diagonals, and 3D problems with cuboids and pyramids. Every method comes with a clear diagram and step-by-step worked examples. It ends with a summary, a keyword guide and exam tips.

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• Main Notes · 21 pages

  Main Notes

  The full notes: one idea per page, a worked example beside every rule.

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• Cheatsheet · 1 page

  Cheatsheet

  The whole topic on a page or two, for the night before.

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• Worksheet · 29 pages

  Worksheet

  Practice questions in the order the notes teach them.

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• Solutions · 23 pages

  Solutions

  Every worksheet question worked in full.

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Topics covered

• Right-angled triangles and the hypotenuse
• Pythagoras’ theorem
• Finding the hypotenuse
• Finding a shorter side
• Real-world problems (ladders and distances)
• Pythagorean triples
• Testing whether a triangle is right-angled
• Acute, right and obtuse triangles
• Height of isosceles and equilateral triangles
• Diagonals of rectangles
• Exact answers in surd form
• Pythagoras in 3D (cuboids and pyramids)

Format

Print-ready PDF

Items

4

Delivery

By email