5.3 Trade Routes and Pasta Anyone?

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5-3 Inequalities in One Triangle

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Presentation transcript:

5.3 Trade Routes and Pasta Anyone? Geometry 5.3 Trade Routes and Pasta Anyone?

5.3: The Triangle Inequality Theorem Objectives Explore the relationships between the side lengths of a triangle and the measures of its interior angles. Prove the Triangle Inequality Theorem

3, 4, 5: Right Triangle: 5 2 = 3 2 + 4 2 6, 7, 8: Acute Triangle: 8 2 < 6 2 + 7 2 6, 8, 11: Obtuse Triangle: 11 2 > 6 2 + 8 2 4, 6, 7: Acute Triangle: 7 2 < 4 2 + 6 2

Relationship Between Type of Triangle and Lengths of Sides Acute Triangle 𝑐 2 < 𝑎 2 + 𝑏 2 Right Triangle 𝑐 2 = 𝑎 2 + 𝑏 2 Obtuse Triangle 𝑐 2 > 𝑎 2 + 𝑏 2

Problem 1: Who is Correct? Together #1 Straw Activity Worksheet (5 Minutes) Tear the straws to form the triangles Answer the questions on the back Investigation 1: What Is the Shortest Path from A to B? The sum of the lengths of any two sides of a triangle is greater than the lengths of the third side.

Problem 1: Who is Correct? #5-6 Together (Discuss) #7 On Your Own (1 Minute) 2+2.4>5.1 Not a triangle 7+1.9>9.2 Not a triangle

Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the lengths of the third side. A B C 𝐴𝐵+𝐴𝐶>𝐵𝐶 𝐴𝐶+𝐵𝐶>𝐴𝐵 𝐵𝐶+𝐴𝐵>𝐴𝐶

Proof of Triangle Inequality Thm

Square root both sides (7) Addition Property (9 & 10) Segment Addition Substitution (11 & 12)

Formative Assessment Skills Practice 5.3 Problem Set Pg. 491-494 (1-22) Due Today Reminder The shortest side is opposite the smallest angle The largest angle is opposite the longest side