1. Warm ups Choose the plane parallel to plane MNR. Choose the segment skew to MP. Classify the relationship between <1 and <5. Classify the relationship between <3 and <8. Classify the relationship between <4 and <6.

2. 3-2 ANGLES AND PARALLEL LINES Objective: Use theorems to determine 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: m<15 = 51 <15 is congruent to <11 Corresponding Angles Postulate m<15 = m<11 Definition of congruent angles m<15 = 51 Substitution

5. 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

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

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

8. Parallel Lines and Angle Pairs

9. Alternate Interior Angles Theorem

10. 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

11. 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.

12. 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

13. 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

14. Example 3 continued 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

15. A. ALGEBRA If m<1 = 9x + 6, m<2 = 2(5x – 3), and m<3 = 5y + 14, find x. Try with a Mathlete A.x = 9 B.x = 12 C.x = 10 D.x = 14

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

17. Concept

18. Homework Pg. 183 # 11 – 19, 25, 27, 29, 36, 43, 46