1. Homework Quiz

2. Strategy for solving algebraic problems: Step 1 – Identify the angle relationship. Step 2 – Congruent or Supplementary? Step 3 – Write an equation and solve.

3. (3y + 55)˚ (2y+15)˚ WARM- UP:

4. If 2 parallel lines are cut by a transversal, then: corresponding angles ______________________ alternate interior angles _____________________ alternate exterior angles _____________________ consecutive interior angles ___________________ 1 2 4 3 5 6 8 7 REVIEW:

5. 3.5 Proving Lines Parallel Objectives: 1.Prove lines are parallel Vocabulary: none

6. The converse is also true: If: corresponding angles are congruent, alternate interior angles are congruent, alternate exterior angles are congruent, consecutive interior angles are supplementary, then the lines are parallel. 3.5 Proving Lines Parallel

7. Converse: Corresponding Angle Postulate Alternate Exterior Angle Theorem Alternate Interior Angle Theorem Consecutive Interior Angle Theorem

8. Determine which lines, if any, are parallel. Answer: Example 1:

9. Determine which lines, if any, are parallel. Answer: Your Turn: Pair-Share

10. GUIDED PRACTICE for Example 1 1. Is there enough information in the diagram to conclude that m n ? Explain. ANSWER Yes. m n because the angle corresponding to the angle measuring 75 o also measures 75 o since it forms a linear pair with the 105 o angle. So, corresponding angles are congruent and the Corresponding Angles Converse says the lines are parallel.

11. GUIDED PRACTICE for Example 1 Can you prove that lines a and b are parallel? Explain why or why not with your partner. 3. Yes; Alternate Exterior Angles Converse. ANSWER

12. GUIDED PRACTICE for Example 1 Yes; Corresponding Angles Converse. ANSWER 4.

13. GUIDED PRACTICE for Example 1 No; Supplementary angles do not have to be congruent. ANSWER 5. m 1 + m 2 = 180°

14. ALGEBRA Find x and m  ZYN so that Example 2: x=15 makes them parallel

15. ALGEBRA Find x and m  GBA so that Answer: Your Turn:

16. y=9

18. EXIT SLIP: Which lines, if any, are parallel? WHY? 1. 2. 3. 4.

19. Geometry HOMEWORK: pg. 211 #8-22 even

20. Homework Quiz!

21. 3.2 Extension: Proving Parallel Line/Angle Relationships Corresponding Angles Postulate: When there are _____ lines, corresponding angles are _________. Alternate Interior Angles Theorem: When there are _____ lines, alternate interior angles are _________. Alternate Exterior Angles Theorem: When there are _____ lines, alternate exterior angles are _________. Consecutive Interior Angles Theorem: When there are ______ lines, consecutive interiors angles are _____________ to each other

22. If two lines are parallel, prove alternate interior angles are congruent. Given: m  n Prove:  4   5 Prove alternate interior angles are congruent. 12 3 4 5 6 7 8 n m m  n Given

23. Prove alternate exterior angles are congruent. 12 3 4 5 6 7 8 n m m  n Given If two lines are parallel, prove alternate exterior angles are congruent. Given: m  n Prove:  1   8

24. Ways of Proving Lines Parallel Four ways to prove two lines are parallel: 1. Show one pair of corresponding angles are Congruent 2. Show one pair of alternate interior angles are Congruent 3. Show one pair of alternate exterior angles are Congruent 4. Show one pair of consecutive interior angles are Supplementary – add up to 180°

25. Converse: Corresponding Angle Postulate Alternate Exterior Angle Theorem Alternate Interior Angle Theorem Consecutive Interior Angle Theorem

26. StatementsReasons 1. Given 2. Given 3. Def. of vertical angles 4. Transitive Prop. 5. Alternate Interior Angles Converse

27. StatementsReasons 1 4 5 1. <1 and <4 are supp. 1. Given 2. <1 and <5 are supp. 2. Given 3. Reflexive Prop. 4. Def. of supp. angles 5. Alternate Interior Angles Converse

28. Around the Room -5 proofs posted around the room (2 sets of each) -Find 2 people to work with and start at one of the proofs (no more than 3 people at one proof) -Fill in the reasons to the statements -Copy the problems, reasons, and statements into your notebook!

29. Homework -Create your own proof -Follow the directions on the sheet -Write the full proof on the back of the sheet -Given, Prove, and Diagram should be on the front -Due tomorrow- worth 5 points!