1. EXAMPLE 1
Relate side length and angle measure
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?
SOLUTION
The longest side and largest angle are opposite each other.
The shortest side and smallest angle are opposite each other.

2. EXAMPLE 2
Standardized Test Practice
SOLUTION
Draw a diagram and label the side lengths. (See diagram on next slide.) The peak angle is opposite the longest side so, by Theorem 5.10, the peak angle is the largest angle.

3. Standardized Test Practice
EXAMPLE 2
Standardized Test Practice
The sum of the angle measures is 180 , so the third angle measure is 180 – ( ) = 75 . You can now label the angle measures in your diagram. o o o o o
The greatest angle measure is 75 , so the correct answer is C. o

4. GUIDED PRACTICE
for Examples 1 and 2 1.
List the sides of RST in order from shortest to longest.
ST, RS, TR
ANSWER

5. GUIDED PRACTICE for Examples 1 and 2 2.
Another stage prop is a right triangle with sides that are 6, 8, and 10 feet long and angles of 90 , about 37 , and about 53 . Sketch and label a diagram with the shortest side on the bottom and the right angle at the left. o 2.
ANSWER

6. EXAMPLE 3
Find possible side lengths
ALGEBRA
A triangle has one side of length 12 and another of length 8. 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.

7. EXAMPLE 3
Find possible side lengths
Small values of x
Large values of x
x + 8
> 12
x > 4
8 + 12
> x
20 > x,
or x < 20
The length of the third side must be greater than 4 and less than 20.
ANSWER

8. GUIDED PRACTICE for Example 3 3. 4 < x < 26 ANSWER
A triangle has one side of 11 inches and another of 15 inches. Describe the possible lengths of the third side.
4 < x < 26
ANSWER

9. Daily Homework Quiz
In Exercises 1 and 2, list the sides or angles in order
from least to greatest. 1.
ANSWER
AB, BC, AC

10. Daily Homework Quiz 2.
ANSWER
R, T, S

11. Daily Homework Quiz
Tell whether the side lengths can form a triangle.
m, 35 m, 18 m
ANSWER
yes
ft, 3 ft, 6 ft
ANSWER no

12. Daily Homework Quiz
5. Jeremy wants to build a triangular toy using sticks.
He has one stick that is 12 inches and another that
is 10 inches. What are the possible lengths of the
third side of the triangle?
ANSWER
greater than 2 in. and less than 22 in.