|
|
| (5 intermediate revisions by 3 users not shown) |
| Line 1: |
Line 1: |
| − | The Pythagorean Inequality is a generalization of the [[Pythagorean Theorem]]. The Theorem 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>. The Inequality extends this to [[obtuse triangle| obtuse]] and [[acute triangle]]s. The inequality says:
| + | #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]]
| |
