1. 3.3 Parallel Lines and Transversals Proving angles congruent with parallel lines

2. Corresponding Angles Postulate If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 1 2 3 4 5 6 7 8

3. Alternate Interior Angles If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent. 1 2 3 4 5 6 7 8

4. Alternate Exterior Angles If two parallel lines are cut by a transversal, then the pairs of alternate exterior interior angles are congruent. 1 2 3 4 5 6 7 8

5. Consecutive Interior Angles If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles are supplementary. 1 2 3 4 5 6 7 8

6. Perpendicular Transversal If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other line. If k // l and k m, kl then l m. 9 10 11 12 m

7. Given: p // q Prove: #1. p // q #1.Given 3 1 5 6 7 8 4 2

8. Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2. 5 6 7 8 4 2

9. Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 4 2

10. Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 #3. 4 2

11. Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 #3.#3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent.

12. Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 #3.#3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent. #4.

13. Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 #3.#3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent. #4.#4.Def. of congruent

14. Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 #3.#3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent. #4.#4.Def. of congruent #5.

15. Given: p // q Prove: #1. p // q #1.Given 3 1 #2.#2.Linear pairs 5 6 are Supplementary 7 8 #3.#3.If two parallel lines 4 2 are cut by a transversal, then Corr. Angles are congruent. #4.#4.Def. of congruent #5.#5.Substitution

16. Solve for x 1

17. X

18. Homework Page 146-148 #8 – 10, 11- 27 odd, #8 – 10, 11- 27 odd, 29, 31 29, 31

19. Homework Page 146-149 #12 – 28 even, 33- 44 33- 44