# Pythagorean theorem

states:

If $\triangle ABC$ is a right triangle, then the http://planetmath.org/node/1087square 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.

 $AC^{2}=AB^{2}+BC^{2}.$

Cosines law is a generalization of Pythagorean theorem for any triangle. It implies that the converse of Pythagorean theorem also holds: if the sides of a triangle satisfy $a^{2}+b^{2}=c^{2}$ 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 Theorem 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