Difference between revisions of "Triangle Inequality"

(Added first intermediate example problem)
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=== Intermediate Problems ===
=== Intermediate Problems ===
* [[2003_AIME_I_Problems/Problem_11 | 2003 AIME I Problem 11]]
* [[2003_AIME_I_Problems/Problem_11 | 2003 AIME I Problem 11]]
== Geometry Resources ==
=== Introductory ===
* [http://www.artofproblemsolving.com/Books/AoPS_B_Item.php?page_id=9 Introduction to Geometry] by [[Richard Rusczyk]]
* [http://www.artofproblemsolving.com/Classes/AoPS_C_ClassesS.php#beggeom AoPS Introduction to Geometry course] -- Based on the lessons in the book listed above by the same title.

Revision as of 16:39, 7 August 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

Intermediate Problems

Geometry Resources


See Also

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