Pythagoras' theorem Cambridge IGCSE Mathematics revision
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In plain words
In any right-angled triangle, the three sides are tied together by one rule. Square the two shorter sides and add them, and you get the square of the longest side. Know any two sides and you can find the third.
Three things to know
- a² + b² = c², where c is the hypotenuse: the longest side, opposite the right angle.
- To find the hypotenuse: square, add, square root.
- To find a shorter side: square, subtract, square root.
Worked example
A right-angled triangle has a hypotenuse of 10 cm and one side of 6 cm. Find the third side.
- It's a shorter side, so subtract: 10² − 6² = 100 − 36 = 64.
- Take the square root.
- 8 cm.
Tips and tricks
- Decide first whether you want the hypotenuse (add) or a shorter side (subtract).
- The hypotenuse must be the longest side. If your answer makes a shorter side longer than it, you added when you should have subtracted.
It lands in your notebook with its questions as flashcards.
Pythagoras' theorem: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
The shorter sides of a right-angled triangle are 3 cm and 4 cm. What is the hypotenuse?
√(9 + 16).
Which side of a right-angled triangle is the hypotenuse?
It is always the longest.
A right-angled triangle has hypotenuse 13 cm and one side 5 cm. What is the third side?
√(169 − 25).
The shorter sides are 6 cm and 8 cm. What is the hypotenuse?
√(36 + 64).
Is a triangle with sides 5, 6 and 8 right-angled?
5² + 6² = 61, but 8² = 64.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
3 questions, 7 marks. Write your answers on paper, then check them.
Pythagoras' theorem
Cambridge IGCSE Mathematics 0580 · 7 marks · papermunch.org
Name ______________________________ Date ______________
The two shorter sides of a right-angled triangle are 5 cm and 12 cm. Find the hypotenuse.[2]
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13 cm. √(25 + 144).
A right-angled triangle has a hypotenuse of 15 cm and one side of 9 cm. Find the other side.[2]
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12 cm. √(225 − 81).
A ladder 5 m long leans against a wall with its foot 1.5 m from the wall. How high up the wall does it reach?[3]
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4.77 m. √(25 − 2.25).
Answers: Pythagoras' theorem
- 1. 13 cm. √(25 + 144).
- 2. 12 cm. √(225 − 81).
- 3. 4.77 m. √(25 − 2.25).