IGCSE Pythagoras Theorem: Complete Guide for Cambridge IGCSE Mathematics

IGCSE Pythagoras theorem is a fundamental geometry topic in Cambridge IGCSE Mathematics that appears in both Paper 2 and Paper 4. Mastering Pythagorean theorem, finding missing sides, and right-angled triangles is essential for solving geometry problems.

This comprehensive IGCSE Pythagoras theorem guide covers everything you need to know, including the theorem formula, finding hypotenuse, finding shorter sides, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to use Pythagoras theorem to find missing sides in right-angled triangles, identify right-angled triangles, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Geometry practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Pythagoras Theorem Matters

IGCSE Pythagoras theorem is an essential geometry topic. Here’s why it’s so important:

• High frequency topic: Pythagoras questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for right-angled triangle problems
• Exam weight: Typically worth 4-7 marks per paper
• Real-world applications: Used in construction, navigation, and engineering
• Problem-solving skills: Develops geometric reasoning

Key insight from examiners: Students often confuse which side is the hypotenuse or make calculation errors. This guide will help you master these systematically.

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Understanding Pythagoras Theorem

Pythagoras theorem: In a right-angled triangle, the square of the hypotenuse equals the sum of squares of the other two sides.

Formula: a² + b² = c² where c is the hypotenuse (longest side, opposite the right angle)

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Finding the Hypotenuse

Example 1: Find the length of the hypotenuse in a right-angled triangle with sides 3 cm and 4 cm.

Solution: c² = a² + b² c² = 3² + 4² = 9 + 16 = 25 c = √25 = 5 cm

Answer: 5 cm

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Finding a Shorter Side

Example 2: In a right-angled triangle, the hypotenuse is 13 cm and one side is 5 cm. Find the other side.

Solution: a² + b² = c² 5² + b² = 13² 25 + b² = 169 b² = 144 b = √144 = 12 cm

Answer: 12 cm

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Identifying Right-Angled Triangles

If a² + b² = c², then the triangle is right-angled.

Example 3: Is a triangle with sides 6, 8, 10 right-angled?

Solution: Check: 6² + 8² = 36 + 64 = 100 10² = 100 Since 6² + 8² = 10², the triangle is right-angled.

Answer: Yes

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Common Examiner Traps

• Hypotenuse confusion - Hypotenuse is always the longest side, opposite the right angle
• Formula errors - Remember: a² + b² = c² (not a + b = c)
• Calculation errors - Double-check squares and square roots

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Practice Questions

Question 1

Find the hypotenuse of a right-angled triangle with sides 6 cm and 8 cm.

Solution: c² = 6² + 8² = 36 + 64 = 100 c = 10 cm

Answer: 10 cm

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📞 Ready to turn shaky Pythagoras skills into exam-ready confidence? Book a free IGCSE maths trial and accelerate your revision plan.

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Frequently Asked Questions About IGCSE Pythagoras Theorem

What is Pythagoras theorem?

Pythagoras theorem states: In a right-angled triangle, a² + b² = c² where c is the hypotenuse.

What is the hypotenuse?

The hypotenuse is the longest side of a right-angled triangle, opposite the right angle.

How do I find the hypotenuse?

Use c = √(a² + b²) where a and b are the shorter sides.

How do I find a shorter side?

Use a = √(c² - b²) where c is the hypotenuse and b is the other side.

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Right-Angled Trigonometry: Complete Guide - Master trigonometry
• IGCSE Similarity: Complete Guide - Master similar triangles
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Pythagoras Theorem with Tutopiya

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