Lesson 5.6: Inequalities in One
Triangle
Rapid fire Geometry
Longest-Side Largest Angle Theorem
• Longest Side-Largest Angle Theorem:
Practice
• List the angles from least to greatest.
D
A
26
38
5
B
E
48
C
12
F
Practice
• For △ABC,
AB = 8
BC = 10
AC = 9.
What is the order of angles from smallest to largest
in this triangle?
SOL Question
A) m∠A is greatest
B) m∠C is greatest
C) m∠A is least
D) m∠C is least
Triangle Inequality Theorem
• Triangle Inequality Theorem:
• Range of possible values:
Practice
• Which set of side lengths will make a triangle?
A)
B)
C)
D)
E)
5m, 5m, 8m
3m, 3m, 3m
17m, 28m, 20m
35m, 21m, 14m
11m, 19m, 20m

Practice
• One side of a triangle is 12m, another 15. What is
the possible range of values of the third side?
SOL Practice
• Which of the following could be the lengths of the
sides of ABC?
A) AB = 12, BC = 15, AC = 2
B) AB = 9, BC = 15, AC = 4
C) AB = 150, BC = 100, AC = 50
D) AB = 10, BC = 8, AC = 12
Lesson 5.7: Inequalities in Two
Triangles
Hinge Theorem
• Hinge Theorem:
Practice
• Which options are possible side lengths for EF?
A)
B)
C)
D)
12
14
16
18
A
D
15
100o
B
C
E
F
Application
• A rubber band is placed between a door and
doorway so to stretch when opened. Will the rubber
band be stretched further when the door is opened
65o or 68o? Why?
Converse of Hinge Theorem
• Converse of Hinge Theorem:
Practice
• Complete the inequality. Figures not drawn to scale:
D
∠A __ ∠E
5
A
5
B
E
12
9
C
13
12
F
Practice
• Complete the inequality: ∠QRT __ ∠SRT
Q
14
R
S
15
T
Algebraically
• What are the possible values for x?
7
3x + 15
75o
16
Challenge
• Complete the following inequality: AB ___ EF. Explain
why this solution is correct.
A
D
x+y
x
B
2y
C
E
2x
F
Classwork
• Lesson 5.6, #1 – 7
Lesson 5.7, #1 – 6
Homework
• p. 345, #5 – 15
Chapter 5 quiz next class.
• Lesson 7.1, #1 – 7