1. Recognize and apply properties of inequalities to the measures of angles of a triangle.
Recognize and apply properties of inequalities to the relationships between angles and sides of a triangle.
Lesson 2 MI/Vocab

2. Lesson 2 KC1

3. Compare Angle Measures
Determine which angle has the greatest measure.
Plan Use properties and theorems of real numbers to compare the angle measures.
Lesson 2 Ex1

4. Determine which angle has the greatest measure.
B.  3
C.  5
D.  4 A B C D
Lesson 2 CYP1

5. Lesson 2 TH1

6. Exterior Angles
Lesson 2 Ex2

7. Exterior Angles
Since 11 and 9 are vertical angles, they have equal measure, so m14 > m9. m9 > m6 and m9 > m7, so m14 > m6 and m14 > m7.
Lesson 2 Ex2

8. Exterior Angles
Lesson 2 Ex2

9. Exterior Angles
Lesson 2 Ex2

10. Lesson 2 TH2

11. Side-Angle Relationships
A. Determine the relationship between the measures of RSU and SUR.
Lesson 2 Ex3

12. Side-Angle Relationships
B. Determine the relationship between the measures of TSV and STV.
Lesson 2 Ex3

13. Side-Angle Relationships
C. Determine the relationship between the measures of RSV and RUV.
Theorem 5.9
Theorem 5.9
Addition Property of Inequality
Angle Addition
Lesson 2 Ex3

14. Side-Angle Relationships
Lesson 2 Ex3

15. A B C D A. B. C.
D. cannot be determined
Lesson 2 CYP3

16. AED and EAD. A. mAED < mEAD B. mAED = mEADC D
A. mAED < mEAD
B. mAED = mEAD
C. mAED > mEAD
D. cannot be determined
Lesson 2 CYP3

17. EAB and EDB. A. mEAB < mEDB B. mEAB = mEDBC D
A. mEAB < mEDB
B. mEAB = mEDB
C. mEAB > mEDB
D. cannot be determined
Lesson 2 CYP3

18. Lesson 2 TH3

19. Angle-Side Relationships
HAIR ACCESSORIES Ebony is following directions for folding a handkerchief to make a bandana for her hair. After she folds the handkerchief in half, the directions tell her to tie the two smaller angles of the triangle under her hair. If she folds the handkerchief with the dimensions shown, which two ends should she tie?
Lesson 2 Ex4

20. Angle-Side Relationships
Theorem 5.10 states that if one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the angle opposite the shorter side. Since X is opposite the longest side it has the greatest measure.
Answer: So, Ebony should tie the ends marked Y and Z.
Lesson 2 Ex4