## Geo Chap 5 5-6

##### Created by:

lanashif  on January 22, 2010

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# Geo Chap 5 5-6

 Theorem 5-10If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side
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Theorem 5-10 If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side
Theorem 5-11 If one angle of a triangle is larger than the other angle, then the side opposite the larger angle is longer than the side opposite the smaller angle
Theorem 5-12 Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
Theorem 5-13 Hinge Theorem If two sides of one triangle are congruent to sides of another triangle, and the included angle of the first is larger than the included angle of the second, then the third side of the first is longer than the third side of the second.
Theorem 5-14 Converse of the Triangle Hinge Theorem If two sides of one triangle are congruent to two sides of another triangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second.
Indirect Proof Make a temporary assumption that what you are trying to prove is false. Reason logically until a contradiction is reached. In this way, the statement to be proven is shown to be true.

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