Theorem

Pythagoras' theorem

Geometry • Triangle • Pythagoras Theorem

Formula

a^{2} + b^{2} = c^{2}

In a triangle right-angled at

B

A B^{2} + B C^{2} = A C^{2}

, where

A C

is the hypotenuse. The converse also holds: if

A B^{2} + B C^{2} = A C^{2}

then the angle at

B

9 0^{\circ}

How to use it

1Identify the hypotenuse first: it is opposite the right angle and is the longest side.
2Use the converse to TEST whether a triangle is right-angled.
3Recognise common triples $(3, 4, 5)$ , $(5, 12, 13)$ , $(8, 15, 17)$ and their multiples to skip the arithmetic.

A right-angled triangle has legs

6

and

8

. Find the hypotenuse.

Step-by-step

1
$c^{2} = 6^{2} + 8^{2} = 36 + 64 = 100$
Why: The right angle is between the legs, so they are the two squared terms.
2
$c = 10$

Answer

10

Watch out

Applies ONLY to right-angled triangles. Putting the wrong side in the

c

position is the most common error.

Builds on

Also known as

pythagorean theorem, hypotenuse formula