Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Theorem 5.10: If one side of a triangle is longer than the other side, then the angle opposite the longest side is _______ than the angle opposite the shorter side. A C B 8 5

Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Theorem 5.11: If one angle of a triangle is larger than another angle, then the side opposite the larger angle is _______ than the side opposite the smaller angle. A C B 50o 30o

Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Example 1 Write measurements in order from least to greatest Write measurements of the triangle in order from least to greatest. D F E 12 22 13 a. 57o A C B 87o 36o b. Solution

Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Example 1 Write measurements in order from least to greatest Write measurements of the triangle in order from least to greatest. D F E 12 22 13 a. 57o A C B 87o 36o b. Solution

Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Checkpoint. Write the measurements of the triangle in order from least to greatest. 34o A C B 99o 47o

Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Checkpoint. Write the measurements of the triangle in order from least to greatest. 45o P R Q 80o 55o

Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Theorem 5.12: Triangle Inequality Theorem A C B The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Example 2 Find possible side lengths A triangle has one side of length 14 and another of length 10. Describe the possible lengths of the third side. Solution Let x represent the length of the third side. Draw diagrams to help visualize the small and large values of x. Then use the Triangle Inequality Theorem to write and solve inequalities. Small values of x Large values of x The length of the third side must be _______________________________. greater than 4 and less than 24

Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Checkpoint. Complete the following exercise A triangle has one side 23 meters and another of 17 meters. Describe the possible lengths of the third side. Small values of x Large values of x The length of the third side must be greater than 6 meters or less than 40 meters

Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Theorem 5.13: Exterior Angle Inequality Theorem The measure of an exterior angle of a triangle is greater than the measure of either of the nonadjacent interior angles.

Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Example 3 Relate exterior and interior angles Solution So, by the Exterior Angle Inequality Theorem, _____ > 70o and ______>_____.

Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Checkpoint. Complete the following exercise

Use Inequalities in a Triangle 5.5 Use Inequalities in a Triangle Pg. 299, 5.5 #1-23