1. Lesson 3-2 Angles and Parallel Lines

2. Ohio Content Standards:

3. Formally define geometric figures.

4. Ohio Content Standards: Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines.

5. Ohio Content Standards: Recognize the angles formed and the relationship between the angles when two lines intersect and when parallel lines are cut by a transversal.

6. Postulate 3.1

7. Corresponding Angles Postulate If two parallel lines are cut by a transversal, then each pair of corresponding angles are congruent.

8. Postulate 3.1 Corresponding Angles Postulate If two parallel lines are cut by a transversal, then each pair of corresponding angles are congruent. 1 4 5 8

9. 10 13 14 17 11 12 15 16 x y z

10. Theorem 3.1

11. Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent.

12. Theorem 3.1 Alternate Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate interior angles are congruent. 34 5 6

13. Theorem 3.2

14. Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary.

15. Theorem 3.2 Consecutive Interior Angles Theorem If two parallel lines are cut by a transversal, then each pair of consecutive interior angles is supplementary. 34 56

16. Theorem 3.3

17. Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate exterior angles are congruent.

18. Theorem 3.3 Alternate Exterior Angles Theorem If two parallel lines are cut by a transversal, then each pair of alternate exterior angles are congruent. 12 78

19. Theorem 3.4

20. Perpendicular Transversal Theorem In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other.

21. Theorem 3.4 Perpendicular Transversal Theorem In a plane, if a line is perpendicular to one of two parallel lines, then it is perpendicular to the other. l n m

22. V 65° R P U S 60° M T N Q

23. 6 7 5 m p q n

24. Assignment: Pgs. 136-138 14-34 evens, 48-58 evens