Difference between revisions of "Triangle Inequality"

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The '''Triangle Inequality''' says that in a nondegenerate triangle <math>\displaystyle ABC</math>:
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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.
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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 10:13, 14 July 2006

The Triangle Inequality says that in a nondegenerate triangle $\displaystyle ABC$:

$\displaystyle AB + BC > AC$

$\displaystyle BC + AC > AB$

$\displaystyle AC + AB > BC$

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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