1. Angles formed by Parallel Lines and Transversals

2. Learning Targets  Students should be able to… Prove and use theorems about the angles formed by parallel lines and a transversal.

3. Warm-up

4. Homework Check

8. 3.1 Quiz Time!  Put everything away.  It should only take about 5-10 minutes to complete!

9. Discovery! 2 4 1 3 6 5 7 8

10. 2 4 1 3 6 5 7 8 Use a protractor to measure each angle!

11. Conclusion  What can you conclude about these types of angles?  Corresponding angles are congruent!!

12. Discovery! 2 4 1 3 6 5 7 8 Use a protractor to measure each angle!

13. Conclusion  What can you conclude about these types of angles?  Alternate Exterior Angles are congruent!!

14. Discovery! 2 4 1 3 6 5 7 8 Use a protractor to measure each angle!

15. Conclusion  What can you conclude about these types of angles?  Alternate Interior Angles are congruent!!

16. Discovery! 2 4 1 3 6 5 7 8

17. 2 4 1 3 6 5 7 8

18. Conclusion  What can you conclude about these types of angles?  Vertical Angles are congruent!!

19. Discovery! 2 4 1 3 6 5 7 8

20. Conclusion  What can you conclude about these types of angles?  Consecutive Interior Angles (same side angles) are SUPPLEMENTARY!!

21. You have just discovered… Theorem 2-7-2: Vertical Angle Theorem Postulate 3-2-1: Corresponding Angles Postulate Theorem 3-2-2: Alternative Interior Angles Theorem 3-2-4: Consecutive Interior Angles Theorem 3-2-3: Alternate Exterior Angles

22. Corresponding Angles Postulate  If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent!

23. Alternate Interior Angles Theorem  If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent!

24. Alternate Exterior Angles Theorem  If two parallel lines are cut by a transversal, then the pairs of alternate exterior angles are congruent!

25. Vertical Angle Theorem  If two parallel lines are cut by a transversal, then the pairs of vertical angles are congruent!

26. Let’s Practice!

30. Extra Practice!

34. Wrap up!! Explanations Needed!

35. Homework Assignment  Page 158 – 159 #1 – 4, 6 – 11, 13 – 19, 21, 23 3.1 Re-takes if needed!! Keep studying those angles!!