Pythagorean theorem

If ABC is a right triangleMathworldPlanetmath, then the of the length of the hypothenuse is equal to the sum of the squares of the two legs. In the following picture, the purple squares add up to the same area as the orange one.


Cosines law is a generalizationPlanetmathPlanetmath of Pythagorean theorem for any triangle. It implies that the converseMathworldPlanetmath of Pythagorean theorem also holds: if the sides of a triangle satisfy a2+b2=c2 then the triangle is a right triangle.

Title Pythagorean theorem
Canonical name PythagoreanTheorem
Date of creation 2013-03-22 11:43:09
Last modified on 2013-03-22 11:43:09
Owner drini (3)
Last modified by drini (3)
Numerical id 28
Author drini (3)
Entry type TheoremMathworldPlanetmath
Classification msc 51-00
Classification msc 20G42
Classification msc 16S40
Classification msc 57T05
Classification msc 16W35
Classification msc 81R50
Classification msc 16W30
Synonym Pythagoreas’ theorem
Synonym Pythagoras theorem
Related topic Triangle
Related topic CosinesLaw
Related topic Hypotenuse
Related topic RightTriangle
Related topic PythagoreanTriple
Related topic ProofOfPythagoreasTheorem
Related topic PythagorasTheorem
Related topic PtolemysTheorem
Related topic FirstPrimitivePythagoreanTriplets
Related topic PythagoreanTheoremInInnerProductSpaces
Related topic GeneralizedPythagoreanTheorem