1. Chapter 5.5 Notes: Use Inequalities in a Triangle Goal: You will find possible side lengths of a triangle.

2. Ex.1: Draw an obtuse scalene triangle. Find the largest angle and longest side and mark them in red. Find the smallest angle and shortest side and mark them in blue. What do you notice? 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.

3. Theorem 5.11: 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. Ex.2: You are constructing a stage prop that shows a large triangular mountain. The bottom edge of the mountain is about 27 feet long, the left slope is about 24 feet long, and the right slope is about 20 feet long. You are told that one of the angles is about 46 o and one is about 59 o. What is the angle measure of the peak of the mountain?

4. Ex.3: Three wooden beams will be nailed together to form a brace for a wall. The bottom edge of the brace is about 8 feet, and the sides are about 12 feet and 14 feet. One of the angles measures about 86 o and the other measures about 35 o. What is the angle measure opposite the largest side of the brace? Ex.4: List the sides of ∆RST in order from shortest to longest.

5. Triangle Inequality 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. – The Triangle Inequality Theorem is used to determine whether three side lengths form a triangle.

6. Is it possible for a triangle to have sides with the given lengths? Explain. Ex.5: 3 cm, 7 cm, and 8 cm Ex.6: 3 ft, 6 ft, and 10 ft Ex.7: 4 cm, 6 cm, and 10 cm Ex.8: 6 cm, 9 cm, and 12 cm

7. Ex.9: A triangle has one side of length 12 and another of length 8. Describe the possible lengths of the third side. Ex.10: A triangle has one side of length 11 and another of length 6. Describe the possible lengths of the third side. Ex.11: A triangle has one side of 11 inches and another of 15 inches. Describe the possible lengths of the third side.

8. Ex.12: A triangle has side lengths of (3x + 1), (4x – 2), and (5x + 7). Describe the possible values of x.