Lesson 5.6: Inequalities in One Triangle

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Presentation transcript:

Lesson 5.6: Inequalities in One Triangle Rapid fire Geometry

Longest-Side Largest Angle Theorem

Practice List the angles from least to greatest. D E F A B C 5 12 26 38 48 5 12

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 Range of possible values:

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

 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? 12 14 16 18 A D 15 B C E F 100o

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

Practice Complete the inequality. Figures not drawn to scale: ∠A __ ∠E E 12 F 5 13 A 5 12 B C 9

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

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 B C E F x + y x 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