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Pythagoras: cheat sheet

Area, volume, circles and Pythagoras · The words and methods from the lessons, with an example of each.

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.

a2+b2=c2a^2 + b^2 = c^2
Squares of 9, 16 and 25 on a 3-4-5 triangle
Squares of 9, 16 and 25 on a 3-4-5 triangle

finding a side

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

c=a2+b2b=c2−a2c = \sqrt{a^2 + b^2} \qquad b = \sqrt{c^2 - a^2}

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.

a2+b2  vs  c2a^2 + b^2 \;\text{vs}\; c^2