1. Splash Screen

2. Then/Now You named angle pairs formed by parallel lines and transversals. Use theorems to determine the relationships between specific pairs of angles. Use algebra to find angle measurements.

3. Concept

4. Example 1 Use Corresponding Angles Postulate A. In the figure, m  11 = 51. Find m  15. Tell which postulates (or theorems) you used. Answer:  15  11 Corresponding Angles Postulate m  15 = m  11 Definition of congruent angles m  15 = 51 Substitution

5. Example 1 Use Corresponding Angles Postulate A. In the figure, m  11 = 51. Find m  15. Tell which postulates (or theorems) you used. Answer: m  15 = 51  15  11 Corresponding Angles Postulate m  15 = m  11 Definition of congruent angles m  15 = 51 Substitution

6. Example 1 Use Corresponding Angles Postulate B. In the figure, m  11 = 51. Find m  16. Tell which postulates (or theorems) you used. Answer:  16  15Vertical Angles Theorem  15  11Corresponding Angles Postulate  16  11Transitive Property (  ) m  16=m  11Definition of congruent angles m  16=51Substitution

7. Example 1 Use Corresponding Angles Postulate B. In the figure, m  11 = 51. Find m  16. Tell which postulates (or theorems) you used. Answer: m  16 = 51  16  15Vertical Angles Theorem  15  11Corresponding Angles Postulate  16  11Transitive Property (  ) m  16=m  11Definition of congruent angles m  16=51Substitution

8. Example 1a A.42 B.84 C.48 D.138 A. In the figure, a || b and m  18 = 42. Find m  22.

9. Example 1a A.42 B.84 C.48 D.138 A. In the figure, a || b and m  18 = 42. Find m  22.

10. Example 1b A.42 B.84 C.48 D.138 B. In the figure, a || b and m  18 = 42. Find m  25.

11. Example 1b A.42 B.84 C.48 D.138 B. In the figure, a || b and m  18 = 42. Find m  25.

12. Concept

14. Example 2 Use Theorems about Parallel Lines FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m  2 = 125, find m  3.  2  3 Alternate Interior Angles Theorem m  2 = m  3 Definition of congruent angles 125 = m  3 Substitution Answer:

15. Example 2 Use Theorems about Parallel Lines FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m  2 = 125, find m  3.  2  3 Alternate Interior Angles Theorem m  2 = m  3 Definition of congruent angles 125 = m  3 Substitution Answer: m  3 = 125

16. Example 2 A.25 B.55 C.70 D.125 FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m  2 = 125, find m  4.

17. Example 2 A.25 B.55 C.70 D.125 FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m  2 = 125, find m  4.

18. A. ALGEBRA If m  5 = 2x – 10, and m  7 = x + 15, find x. Example 3 Find Values of Variables  5  7 Corresponding Angles Postulate m  5 = m  7 Definition of congruent angles 2x – 10 = x + 15 Substitution x – 10 =15Subtract x from each side. x =25Add 10 to each side. Answer:

19. A. ALGEBRA If m  5 = 2x – 10, and m  7 = x + 15, find x. Example 3 Find Values of Variables  5  7 Corresponding Angles Postulate m  5 = m  7 Definition of congruent angles 2x – 10 = x + 15 Substitution x – 10 =15Subtract x from each side. x =25Add 10 to each side. Answer: x = 25

20. B. ALGEBRA If m  4 = 4(y – 25), and m  8 = 4y, find y. Example 3 Find Values of Variables  8  6Corresponding Angles Postulate m  8=m  6Definition of congruent angles 4y=m  6Substitution

21. Example 3 Find Values of Variables m  6 + m  4=180Supplement Theorem 4y + 4(y – 25)=180Substitution 4y + 4y – 100=180Distributive Property 8y=280Add 100 to each side. y=35Divide each side by 8. Answer:

22. Example 3 Find Values of Variables m  6 + m  4=180Supplement Theorem 4y + 4(y – 25)=180Substitution 4y + 4y – 100=180Distributive Property 8y=280Add 100 to each side. y=35Divide each side by 8. Answer: y = 35

23. A. ALGEBRA If m  1 = 9x + 6, m  2 = 2(5x – 3), and m  3 = 5y + 14, find x. Example 3 A.x = 9 B.x = 12 C.x = 10 D.x = 14

24. A. ALGEBRA If m  1 = 9x + 6, m  2 = 2(5x – 3), and m  3 = 5y + 14, find x. Example 3 A.x = 9 B.x = 12 C.x = 10 D.x = 14

25. B. ALGEBRA If m  1 = 9x + 6, m  2 = 2(5x – 3), and m  3 = 5y + 14, find y. Example 3 A.y = 14 B.y = 20 C.y = 16 D.y = 24

26. B. ALGEBRA If m  1 = 9x + 6, m  2 = 2(5x – 3), and m  3 = 5y + 14, find y. Example 3 A.y = 14 B.y = 20 C.y = 16 D.y = 24

27. Concept

28. End of the Lesson