Difference between revisions of "Triangle Inequality"
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| − | The '''Triangle Inequality''' says that in a nondegenerate triangle <math>\displaystyle ABC</math>: | + | The '''Triangle Inequality''' says that in a [[nondegenerate]] [[triangle]] <math>\displaystyle ABC</math>: |
<math>\displaystyle AB + BC > AC</math> | <math>\displaystyle AB + BC > AC</math> | ||
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<math>\displaystyle AC + AB > BC</math> | <math>\displaystyle AC + AB > BC</math> | ||
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| + | That is, the sum of the lengths of any two sides is larger than the length of the third side. | ||
| + | In [[degenerate]] triangles, the [[strict inequality]] must be replaced by "greater than or equal to." | ||
This inequality often shows up in contest problems. | This inequality often shows up in contest problems. | ||
Revision as of 11:13, 14 July 2006
The Triangle Inequality says that in a nondegenerate triangle 
:
That is, the sum of the lengths of any two sides is larger than the length of the third side. In degenerate triangles, the strict inequality must be replaced by "greater than or equal to."
This inequality often shows up in contest problems.
Example Problems
Introductory Problems
See Also
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