Editing Right triangle (section)

===Sides===
[[File:Illustration to Euclid's proof of the Pythagorean theorem2.svg|thumb|The diagram for Euclid's proof of the Pythagorean theorem: each smaller square has area equal to the rectangle of corresponding color.]]
{{main|Pythagorean theorem}}

The three sides of a right triangle are related by the [[Pythagorean theorem]], which in modern algebraic notation can be written

:<math>a^2 + b^2 = c^2,</math>

where <math>c</math> is the length of the ''hypotenuse'' (side opposite the right angle), and <math>a</math> and <math>b</math> are the lengths of the ''legs'' (remaining two sides). [[Pythagorean triple]]s are integer values of <math>a, b, c</math> satisfying this equation. This theorem was proven in antiquity, and is proposition I.47 in [[Euclid's Elements|Euclid's ''Elements'']]: "In right-angled triangles the square on the side subtending the right angle is equal to the squares on the sides containing the right angle."