Section 5.6- Inequalities in One Triangle
Essential Question: What is the relationship between angle measures and segment
lengths in a triangle?
Do Now:
Fill in with the correct inequality sign. (> or <)
8 ____ 6
12 ____ 15
What does this mean?
2 < x < 20
Key Concept: Triangle Inequality Theorem
The _______ of the lengths of any two sides of a triangle is _________________ the
length of the third side
Example 1: Using the Triangle Inequality Theorem
Can a triangle have sides with given lengths?
a. 2m, 6m, and 9m
b. 4 yd, 6 yd, 9 yd
Example 2: Finding Possible Side Lengths
A triangle has side lengths of 4 inches and 7 inches. What is the range of the possible
side lengths?
Case 1- For SMALLEST possible side length, ____________ the two given side lengths.
Case 2- For LARGEST possible side length, _________ the two given side lengths.
Relating Sides and Angles

The longest side and ___________ angle are opposite each other.

The ____________ side and smallest angle are opposite each other.
Example 3: Relating Side Lengths and Angles
Group Work:
Complete #1-5
HW: p. 329-330 # 9, 11, 15-17, 21-23, 27-29, 34, 37-39