1. Can the measure of 5, 7, and 8 be the lengths of the sides of a triangle?
Can the measures 4.2, 4.2, and 8.4 be the lengths of the sides of a triangle?
Can the measures 3, 6, and 10 be the lengths of the sides of a triangle?
Find the range for the measure of the third side of a triangle if two of its sides measure 4 and 13.
Find the range for the measure of the third side of a triangle if two of its sides measure 8.3 and 15.6.
Lesson 5 Menu

2. Apply the SAS Inequality.
Apply the SSS Inequality.
Lesson 5 MI/Vocab

3. Lesson 5 TH1

4. Use SAS Inequality in a Proof
Write a two-column proof.
Given:
Prove:
Lesson 5 Ex1

5. Use SAS Inequality in a Proof
Statements
Reasons 1.
1. Given 2.
2. Alternate interior angles are congruent. 3.
3. Substitution 4.
4. Subtraction Property 5.
5. Given 6.
6. Reflexive Property 7.
7. SAS Inequality
Lesson 5 Ex1

6. Which reason correctly completes the two-column proof?
Prove: AC < AB
Given: m1 < m3 E is the midpoint of
Lesson 5 CYP1

7. Proof: Statements 1. 2. 3. 4. 5. 6. 7. 8. Reasons
1. Given 2. Definition of midpoint 3. Reflexive Property 4. Given 5. Vertical Angle Theorem 6. Definition of congruent angles 7. Substitution 8. _______________
2  3
E is the midpoint of
Lesson 5 CYP1

8. A. SSS Inequality Theorem B. SAS Inequality Theorem
C. Substitution
D. none of the above A B C D
Lesson 5 CYP1

9. Lesson 5 TH2

10. Prove Triangle Relationships
Given:
Prove:
Lesson 5 Ex2

11. Prove Triangle Relationships
Proof:
Statements
Reasons 1.
1. Given 2.
2. Reflexive Property 3.
3. Given 4.
4. Given 5.
5. Substitution 6.
6. SSS Inequality
Lesson 5 Ex2

12. Which reason correctly completes the following proof?
Given: X is the midpoint of ΔMCX is isosceles. CB > CM
Prove:
Lesson 5 CYP2

13. Proof: Statements 1. 2. 3. 4. 5. 6. 7. Reasons
Reasons
1. Given 2. Definition of midpoint 3. Given 4. Definition of isosceles triangle 5. Given 6. Substitution 7. ______________
X is the midpoint of
ΔMCX is isosceles.
Lesson 5 CYP2

14. A. SSS Inequality Theorem B. SAS Inequality Theorem
C. Substitution
D. none of the above A B C D
Lesson 5 CYP2

15. Relationships Between Two Triangles
A. Write an inequality relating mLDM to mMDN using the information in the figure.
Lesson 5 Ex3

16. Relationships Between Two Triangles
In ΔMDL and ΔMDN,
The SSS Inequality allows us to conclude that
Answer: mLDM > mMDN
Lesson 5 Ex3

17. Relationships Between Two Triangles
B. Write an inequality finding the range of values containing a using the information in the figure.
By the SSS Inequality,
Lesson 5 Ex3

18. Relationships Between Two Triangles
SSS Inequality
Substitution
Subtract 15 from each side.
Divide each side by 9.
Also, recall that the measure of any angle is always greater than 0.
Subtract 15 from each side.
Divide each side by 9.
Lesson 5 Ex3

19. Relationships Between Two Triangles
The two inequalities can be written as the compound
inequality
Lesson 5 Ex3

20. A. Compare mWYX and mZYW and write an inequality statement.
A. mWYX < mZYW
B. mWYX = mZYW
C. mWYX > mZYW
D. cannot be determined A B C D
Lesson 5 CYP3

21. B. Find the range of values containing n and write an inequality statement.
C. n > 6
D. 6 < n < 18.3 A B C D
Lesson 5 CYP3

22. Use Triangle Inequalities
HEALTH Doctors use a straight-leg-raising test to determine the amount of pain felt in a person’s back. The patient lies flat on the examining table, and the doctor raises each leg until the patient experiences pain in the back area. Nitan can tolerate the doctor raising his right leg 35° and his left leg 65° from the table. Which foot can Nitan raise higher above the table?
Assume both of Nitan’s legs have the same measurement, the SAS Inequality tells us that the height of the left foot opposite the 65° angle is higher than the height of his right foot opposite the 35° angle. This means that his left foot is raised higher.
Answer: his left foot
Lesson 5 Ex4

23. HEALTH Doctors use a straight-leg-raising test to determine the amount of pain felt in a person’s back. The patient lies flat on the examining table, and the doctor raises each leg until the patient experiences pain in the back area. Megan can lift her right foot 18 inches from the table and her left foot 13 inches from the table. Which leg makes the greater angle with the table? A B C
A. her right leg
B. her left leg
C. neither
Lesson 5 CYP4