1. Lesson 5.6: Inequalities in One Triangle
Rapid fire Geometry

2. Longest-Side Largest Angle Theorem

3. Practice List the angles from least to greatest. D E F A B C 5 12 48 5 12

4. Practice
For △ABC, AB = 8 BC = 10 AC = 9. What is the order of angles from smallest to largest in this triangle?

5. SOL Question A) m∠A is greatest B) m∠C is greatest C) m∠A is least
D) m∠C is least

6. Triangle Inequality Theorem
Range of possible values:

7. Practice Which set of side lengths will make a triangle? 5m, 5m, 8m

8. 
Practice
One side of a triangle is 12m, another 15. What is the possible range of values of the third side?

9. 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

10. Lesson 5.7: Inequalities in Two Triangles

11. Hinge Theorem
Hinge Theorem:

12. Practice Which options are possible side lengths for EF? 12 14 16 18
A D 15
B C E F
100o

13. 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?

14. Converse of Hinge Theorem

15. Practice Complete the inequality. Figures not drawn to scale: ∠A __ ∠E
E 12 F A
B C 9

16. Practice
Complete the inequality:
∠QRT __ ∠SRT Q R
S T 14 15

17. Algebraically
What are the possible values for x? 7
3x + 15
75o 16

18. Challenge
Complete the following inequality: AB ___ EF. Explain why this solution is correct.
A D
B C E F
x + y x
2y x

19. Classwork
Lesson 5.6, #1 – 7 Lesson 5.7, #1 – 6

20. Homework
p. 345, #5 – 15 Chapter 5 quiz next class.
Lesson 7.1, #1 – 7