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# Triangle Inequality Theorem - Geometric Inequalities

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The length of one side of a triangle is less than the sum of the lengths of the other two sides

Relationships of a Triangle
The placement of a triangle’s sides and angles is very important. We have worked with triangles extensively, but one important detail we have probably overlooked is the relationship between a triangle’s sides and angles. These angle-side relationships characterize all triangles, so it will be important to understand these relationships in order to enrich our knowledge of triangles.
Angle-Side Relationships
If one side of a triangle is longer than another side, then the angle opposite the longer side will have a greater degree measure than the angle opposite the shorter side.

Converse also true:
If one angle of a triangle has a greater degree measure than another angle, then the side opposite the greater angle will be longer than the side opposite the smaller angle.

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Which of the following may be the lengths of the sides of a triangle?
1) 4,6,10 2) 8,8,16 3) 6,8,16 4) 10,12,14

This lesson also gives an example of how this theorem is used in a geometric inequality proof.
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