---
title: "Pythagoras: cheat sheet"
subtitle: "Area, volume, circles and Pythagoras"
---

# Pythagoras

> The words and methods from this unit, with an example of each.

:::keep-together

**Pythagoras' theorem**: In a right-angled triangle, the squares on the two shorter sides add to the square on the hypotenuse c, the side opposite the right angle.

$$a^2 + b^2 = c^2$$

_Squares of 9, 16 and 25 on a 3-4-5 triangle_

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:::keep-together

**finding a side**: Add the squares for the hypotenuse; subtract for a shorter side. Check: the hypotenuse is the longest.

$$c = \sqrt{a^2 + b^2} \qquad b = \sqrt{c^2 - a^2}$$

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:::keep-together

**right, acute or obtuse**: With c the longest side: equal, right-angled; a² + b² smaller, obtuse; bigger, acute. Pythagorean triples: 3-4-5, 5-12-13, 8-15-17 and multiples.

$$a^2 + b^2 \;\text{vs}\; c^2$$

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