Pythagoras' Theorem for IGCSE Maths
Finding missing sides in right-angled triangles. This subtopic is part of Geometry in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding pythagoras' theorem is
What You Need to Know
Finding missing sides in right-angled triangles. This subtopic is part of Geometry in the Cambridge IGCSE Mathematics 0580 syllabus (both Core and Extended tiers). Understanding pythagoras' theorem is essential for achieving a strong grade in your IGCSE Maths exam.
Understanding Pythagoras' Theorem
Pythagoras' Theorem states that in any right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides: a² + b² = c², where c is the hypotenuse (the side opposite the right angle). It is used to find a missing side, to check whether a triangle is right-angled (given three sides), and extended to 3D problems. Pythagoras appears throughout IGCSE 0580 in Core and Extended papers.
Step-by-Step Method
- 1
Identify the hypotenuse
The hypotenuse is always opposite the right angle. It is the longest side. Label it c.
- 2
Write the theorem
a² + b² = c². Identify which side is unknown.
- 3
Substitute known values
Replace a, b, and/or c with the given measurements.
- 4
Solve for the unknown
Finding hypotenuse: c = √(a² + b²). Finding a leg: a = √(c² − b²).
- 5
Round and check
Round to the required accuracy. Check the hypotenuse is longer than both legs.
Worked Example
Question
A right-angled triangle has legs of 7 cm and 24 cm. Find the hypotenuse. Also, find the missing leg if the hypotenuse is 15 cm and one leg is 9 cm.
Solution
Part 1: c² = 7² + 24² = 49 + 576 = 625 c = √625 = 25 cm Part 2: a² + 9² = 15² a² = 225 − 81 = 144 a = √144 = 12 cm Answers: Hypotenuse = 25 cm; Missing leg = 12 cm
Exam Tips for Pythagoras' Theorem
- The hypotenuse is always opposite the right angle — label it before writing a²+b²=c².
- When finding a leg, subtract: a² = c² − b². A common error is adding instead of subtracting.
- Common Pythagorean triples to recognise: 3-4-5, 5-12-13, 7-24-25, 8-15-17.
- Pythagoras in 3D: find the base diagonal first, then use it in a second right-angled triangle.
Practice Questions
Q1: Find the diagonal of a rectangle with length 16 cm and width 12 cm.
Show hint
Diagonal² = 16²+12² = 256+144 = 400. Diagonal = 20 cm.
Q2: A triangle has sides 5 cm, 12 cm, 13 cm. Is it right-angled? Justify.
Show hint
Check 5²+12² = 25+144=169 = 13². Yes, right-angled.
Q3: A point P is 3 km North and 4 km West of Q. Find the straight-line distance PQ.
Show hint
PQ = √(3²+4²) = √25 = 5 km.
Frequently Asked Questions
What is pythagoras' theorem in IGCSE Maths?
Finding missing sides in right-angled triangles.
Is pythagoras' theorem in the Core or Extended syllabus?
Pythagoras' Theorem is part of the Core and Extended syllabus for IGCSE Mathematics 0580.
How do I revise pythagoras' theorem effectively?
Start with the revision notes to understand key concepts, then work through the worked examples step by step. Finally, practise past paper questions under timed conditions. Teacher Rig recommends spending focused revision sessions on pythagoras' theorem rather than trying to cover everything at once.
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