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4.7 Triangle Inequalities. Theorem 4.10 If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than.

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Presentation on theme: "4.7 Triangle Inequalities. Theorem 4.10 If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than."— Presentation transcript:

1 4.7 Triangle Inequalities

2 Theorem 4.10 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. A B C 5 13 IF BC > AC, then m m<B

3 Theorem 4.11 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. D E F 60°40° IF m m DF

4 10 4 8 C A B Name the angles from largest to smallest.

5 58° 86°37° D EF Name the sides from longest to shortest

6 Theorem 4.12 The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A B C CA + AB > BC AB + BC > CA BC + CA > AB

7 Can the side lengths form a triangle? 3, 5, 9 ? 3, 5, 8 ? 3, 5, 7 ? 5, 7, 13 ? 6, 9, 12 ? 10, 15, 25 ?

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