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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:
| + | #REDIRECT[[Pythagorean inequality]] |
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| − | 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>.
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| − | This inequality is a direct result of the [[Law of Cosines]], although it is also possible to prove without using [[trigonometry]].
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| − | ==See also==
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| − | * [[Triangle]]
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| − | * [[Law of Sines]]
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| − | * [[Law of Cosines]]
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| − | [[Category:Inequality]]
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| − | [[Category:Geometry]]
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| − | [[Category:Theorems]]
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