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.

A

B

C

26 38

48

5

12

D

E F

Practice

• For △ABC,AB = 8BC = 10AC = 9.

What is the order of angles from smallest to largest in this triangle?

SOL Question

A) m∠A is greatestB) m∠C is greatestC) m∠A is leastD) 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) 5m, 5m, 8mB) 3m, 3m, 3m C) 17m, 28m, 20mD) 35m, 21m, 14mE) 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 = 2B) AB = 9, BC = 15, AC = 4C) AB = 150, BC = 100, AC = 50D) 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) 12B) 14C) 16D) 18 100o

A D

15

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:

• Complete the inequality. Figures not drawn to scale:∠A __ ∠E D

E 12 F

Practice

5 13

B C

A

5 12

9

• Complete the inequality:

Q

R

S T

Practice

15

14

∠QRT __ ∠SRT

Algebraically

• What are the possible values for x?

7

16

75o

3x + 15

A D

B C E F

• Complete the following inequality: AB ___ EF. Explain why this solution is correct.

Challenge

x x + y

2y 2x

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