Pythagorean theorem

Pythagorean theorem states:

If $\mathrm{△}ABC$ 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.

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

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