Triangle Inequality

Revision as of 16:36, 7 August 2006 by MCrawford (talk | contribs) (Added first intermediate example problem)

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

Intermediate Problems


See Also

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