stylistic:tone, information:classification
Sides

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

where c {\displaystyle c} is the length of the hypotenuse (side opposite the right angle), and a {\displaystyle a} and b {\displaystyle b} are the lengths of the legs (remaining two sides). Pythagorean triples are integer values of a, b, c {\displaystyle a,b,c} satisfying this equation. This theorem was proven in antiquity, and is proposition I.47 in 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."