1. Math II 7.5 Parallel Lines and Transversals

2. Activity Look at your assignment.

3. Activity use a straight edge to draw a line that cuts through the first pair of lines.

4. Activity You have made 8 angles!

5. Activity Use your protractor to measure and record the size of each angle.

6. Activity Repeat this process with the Second set of parallel lines on your worksheet

7. Activity With the 3 rd set of lines Start by drawing a line through them. But this time we won’t use your protractor.

8. Activity Pick a symbol. # θ۞ ☺ ♥  ♫ Any symbol you like It must be school appropriate!

9. Draw that symbol in one of the angles. Now draw it in any other angle that would have the same measure.

10. Activity Pick a different symbol. $ &     Any symbol you like It must be school appropriate!

11. Draw that symbol in one of the angles that does not have a symbol. Now draw it in any other angle that would have the same measure.

12. Activity Do you notice any patterns? Do you think this will always work?

13. So your last picture... should look something like this... 12 34 56 78        

14. Transversal The line you drew has a special name… It is a transversal.

15. Lines cut by a transversal may or may not be parallel.

16. 98 percent of what we do in Math with transversals will involve parallel Lines

17. You will know they are parallel because they will tell you, or they will draw an extra arrow on the lines

18. Transversals can intersect any number of lines.

19. When a transversal intersects a line, four angles are formed 12 34

20. angles across from each other are called Vertical Angles. 12 34 ∠ 1 and ∠ 4 are a pair of vertical angles ∠ 2 and ∠ 3 are a pair of vertical angles

21. Based on your discoveries: What can you say about vertical angles? 12 34

22. When a transversal intersects two lines, eight angles are formed 12 34 56 78

23. These are called interior angles 34 56

24. These are called exterior Angles 12 78

25. Corresponding angles are angles in similar locations 12 34 56 78

26. Based on your discoveries: What can you say about corresponding angles? 12 34 56 78

27. Alternate interior Angles 34 56

28. Based on your discoveries: What can you say about alternate interior angles? 34 56

29. Alternate exterior Angles 12 78

30. Based on your discoveries: What can you say about alternate exterior angles? 12 78

31. Consecutive interior Angles 34 56

32. Based on your discoveries: What can you say about Consecutive interior angles? 34 56

33. Things to know: Vertical angles are always Congruent

34. If the lines are parallel then: Corresponding Angles are Congruent

35. If the lines are parallel then: Alternate Interior Angles are Congruent

36. If the lines are parallel then: Alternate Exterior Angles are Congruent

37. If the lines are parallel then: Consecutive Interior Angles are Supplementary

38. Quick summary:         If lines are parallel, then All  ’s are congruent All  ‘s are congruent  +  = 180