Unit 6 Lesson 6 Inequalities in One Triangle CCSS Lesson Goals G-SRT 4: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures Use triangle measurements to decide which side is longest or which angle is largest. ESLRs: Becoming Effective Communicators, Competent Learners and Complex Thinkers

theorem Triangle Angle-Side Relationships Th The longest side of a triangle is opposite the largest angle and the shortest side of a triangle is opposite the smallest angle. A B C shortest side largest angle longest side smallest angle

example Write the measures for the sides of the triangle in order from least to greatest A B C 111o 46o 23o

You Try (not in notes) Write the measures for the sides of the triangle in order from least to greatest T U 10 V 7 11

theorem Exterior Angle Inequality Theorem The measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles. A 1 C B

theorem Exterior Angle Inequality Theorem The measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles. A 1 C B

example 6 7 3 5 4 2 1

example Write an equation or inequality to describe the relationship between the measures of all angles. ao do co bo

Spaghetti and Triangles

Theorem (review) Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A B C A B C A C

Theorem (review) Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A B C B A C B C

Theorem (review) Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle is greater than the length of the third side. A B C A C B A B

example 5, 7, 8 5 + 7 > 8 5 + 8 > 7 7 + 8 > 5 Yes Can a triangle be constructed with sides of the following measures? 5, 7, 8 5 + 7 > 8 5 + 8 > 7 7 + 8 > 5 Yes By the Triangle Inequality Theorem, the sum of the measures of any two sides must by greater than the third side.

example x + 8 > 17 x + 17 > 8 8 + 17 > x x > 9 9 < x A triangle has one side of 8 cm and another of 17 cm. Describe the possible lengths of the third side. x + 8 > 17 x + 17 > 8 8 + 17 > x x > 9 9 < x x > anything 25 > x x < 25 17 8 x By the Triangle Inequality Theorem, the sum of the measures of any two sides must by greater than the third side.

example x + 11 > 16 x + 16 > 11 11 + 16 > x x > 5 5 < x A triangle has one side of 11 in and another of 16 in. Describe the possible lengths of the third side. x + 11 > 16 x + 16 > 11 11 + 16 > x x > 5 5 < x x > anything 27 > x x < 27 16 11 x By the Triangle Inequality Theorem, the sum of the measures of any two sides must by greater than the third side.

Today’s Assignment p. 298: 1 – 5, 7 – 19 o, 25

Lesson 6 Day 2 5.5 worksheet B due in class

Today’s Assignment p. 298: 6 – 20 e, 24, 29 – 31