1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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.

8. 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

9. 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

10. 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.

11. 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 ______>_____.

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

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