Difference between revisions of "Pythagorean Inequality"

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The Pythagorean Inequality is a generalization of the [[Pythagorean Theorem]], which states that in a [[right triangle]] with sides of length <math>a \leq b \leq c</math> we have <math>a^2 + b^2 = c^2</math>.  This Inequality extends this to [[obtuse triangle| obtuse]] and [[acute triangle]]s. The inequality says:
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#REDIRECT[[Pythagorean inequality]]
 
 
For an acute triangle with sides of length <math>a \leq b \leq c</math>, <math>a^2+b^2>c^2</math>. For an obtuse triangle with sides <math>a \leq b \leq c</math>, <math>a^2+b^2<c^2</math>.
 
 
 
This inequality is a direct result of the [[Law of Cosines]], although it is also possible to prove without using [[trigonometry]].
 
 
 
==See also==
 
* [[Triangle]]
 
* [[Law of Sines]]
 
 
 
[[Category:Inequality]]
 
[[Category:Geometry]]
 
[[Category:Theorems]]
 

Latest revision as of 10:08, 10 May 2021

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