1. 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

2. 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

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

4. 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

5. 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

6. 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

7. example 6 7 3 5 4 2 1

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

9. Spaghetti and Triangles

10. 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

11. 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

12. 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

13. 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.

14. 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
> 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.

15. 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
> 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.

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

20. Lesson 6 Day 2
5.5 worksheet B due in class

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