5.4 Inequalities in One Triangle

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Presentation transcript:

5.4 Inequalities in One Triangle

Theorem 5.7 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. B 3.5 cm 5.5 cm A C 7.5 cm AB < BC < AC m<C < m<A < m<B

Theorem 5.8 If one angle of a triangle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

Theorem 5.9 Triangle Inequality The sum of the lengths of any two sides of a triangle is greater than the length of the third side. B Example: cable Minimum length: 300-100=200 ft Maximum Length : 300+100=400 ft A 300 ft 200 < cable < 400 100 ft C