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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.

Remove gray boxes to reveal important information to students.

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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