1. Angles and Parallel Lines LESSON 3–2

2. Lesson Menu Five-Minute Check (over Lesson 3–1) TEKS Then/Now Postulate 3.1:Corresponding Angles Postulate Example 1:Use Corresponding Angles Postulate Theorems:Parallel Lines and Angle Pairs Proof: Alternate Interior Angles Theorem Example 2:Real-World Example: Use Theorems about Parallel Lines Example 3:Find Values of Variables Theorem 3.4: Perpendicular Transversal Theorem

3. Over Lesson 3–1 5-Minute Check 1 A.RST B.PON C.STQ D.POS Choose the plane parallel to plane MNR.

4. Over Lesson 3–1 5-Minute Check 2 A.PM B.TS C.PO D.MQ ___ Choose the segment skew to MP.

5. Over Lesson 3–1 5-Minute Check 3 A.corresponding angles B.vertical angles C.consecutive interior angles D. alternate exterior angles Classify the relationship between  1 and  5.

6. Over Lesson 3–1 5-Minute Check 4 A.alternate interior angles B.alternate exterior angles C.corresponding angles D.consecutive interior angles Classify the relationship between  3 and  8.

7. Over Lesson 3–1 5-Minute Check 5 A.alternate interior angles B.alternate exterior angles C.corresponding angles D.vertical angles Classify the relationship between  4 and  6.

8. Over Lesson 3–1 A.OS B.TS C.NR D.MQ 5-Minute Check 6 Which of the following segments is not parallel to PT?

9. TEKS Targeted TEKS G.6(A) Verify theorems about angles formed by the intersection of lines and line segments, including vertical angles, and angles formed by parallel lines cut by a transversal and prove equidistance between the endpoints of a segment and points on its perpendicular bisector and apply these relationships to solve problems. Mathematical Processes G.1(A), G.1(G)

10. 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.

11. Concept

12. 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

13. 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

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

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

16. Concept

18. 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

19. 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.

20. A. ALGEBRA If m  5 = 2x – 10, and m  7 = x + 15, find x. Explain your reasoning 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

21. 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

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. 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

25. Concept

26. Angles and Parallel Lines LESSON 3–2