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# Pythagorean theorem

Pythagorean theorem states:

If $\triangle ABC$ is a right triangle, then the square 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.

Keywords:

Pythagoras, triangle, right, hypotenuse,leg

Related:

Triangle, CosinesLaw,Hypotenuse,RightTriangle,PythagoreanTriple, ProofOfPythagoreasTheorem, PythagorasTheorem,PtolemysTheorem, FirstPrimitivePythagoreanTriplets, PythagoreanTheoremInInnerProductSpaces, GeneralizedPythagoreanTheorem

Synonym:

Pythagoreas' theorem, Pythagoras theorem

Type of Math Object:

Theorem

Major Section:

Reference

Groups audience:

## Mathematics Subject Classification

51-00*no label found*20G42

*no label found*16S40

*no label found*57T05

*no label found*16W35

*no label found*81R50

*no label found*16W30

*no label found*

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## Attached Articles

## Corrections

link to "square" by akrowne ✓

other name by mathwizard ✓

funny page images by mathwizard ✓

ptolemy's theorem by alozano ✓

Small typo by Poly ✓

other name by mathwizard ✓

funny page images by mathwizard ✓

ptolemy's theorem by alozano ✓

Small typo by Poly ✓

## Comments

## Drawing

I know...

I'll make a graphic when I return home next week

f

G -----> H G

p \ /_ ----- ~ f(G)

\ / f ker f

G/ker f

## Re: Drawing

its been a lot longer than a week!

-apk

## Re: Drawing

heehhe but finally it's done

f

G -----> H G

p \ /_ ----- ~ f(G)

\ / f ker f

G/ker f