1. Properties of Parallel Lines Objectives: Explore relationships of the angles of parallel lines cut by a transversal.

2. parallel lines - two or more co-planar lines that do not intersect Co-planar - lie on same plane

3. m  n  o n m o

4. No - they intersect (cross). a b Are these two lines parallel?

5. No - they will intersect if you extend the lines. d c Are these two lines parallel?

6. It sure looks like they are! f e Are these two lines parallel?

7. transversal - a line that intersects 2 or more lines

8. n Line n is a transversal. It intersects line a & b. b a

9. r Is line r a transversal? b a c Yes - it intersects 3 lines.

10. corresponding angles - two angles on the same side of transversal and on the same side of the parallel lines

11.  1 and  5 are corresponding angles. List the other 3 pairs of corresponding  ’s. 1 4 3 6 2 5 7 8

12. alternate interior angles - angles that are on opposite sides of transversal and between the parallel lines

13.  3 and  6 are alternate interior angles. List the other pair of A.I.A.’s. 1 4 3 6 2 5 7 8 4 & 5

14. alternate exterior angles - angles that are on opposite sides of transversal and not between the parallel lines

15.  1 and  8 are alternate exterior angles. List the other pair of A.E.A.’s. 1 4 3 6 2 5 7 8 2 & 7

16. When parallel lines are cut by a transversal, there are special relationships among the angles formed…..let’s investigate!

17. Compare the measures of pairs of corresponding angles…what do you see? C-17a Corresponding Angle Conjecture : If two parallel lines are cut by a transversal, then C.A.’s are ___________. congruent

18. Compare the measures of pairs of alternate interior angles…what do you see? C-17b Alternate Interior Angle Conjecture : If two parallel lines are cut by a transversal, then A.I.A.’s are ___________. congruent

19. Compare the measures of pairs of alternate exterior angles…what do you see? C-17c Alternate Exterior Angle Conjecture : If two parallel lines are cut by a transversal, then A.E.A.’s are ___________. congruent

20. Sketch this diagram. Write in unknown angle measures. 1 3 4 2 6 5 7 68

21. Measure of  1 =? 1 3 4 2 6 5 7 68

22. Measure of  1 =? 68 3 4 2 6 5 7 68

23. Measure of  2 =? 68 3 4 2 6 5 7 68

24. Measure of  2 =? 68 3 4 112 6 5 7 68

25. Measure of  3 =? 68 3 4 112 6 5 7 68

26. Measure of  3 =? 68 112 4 112 6 5 7 68

27. Measure of  4 =? 68 112 4 112 6 5 7 68

28. Measure of  4 =? 68 112 68 112 6 5 7 68

29. Measure of  5 =? 68 112 68 112 6 5 7 68

30. Measure of  5 =? 68 112 68 112 6 112 7 68

31. Measure of  6 =? 68 112 68 112 6 112 7 68

32. Measure of  6 =? 68 112 68 112 112 112 7 68

33. Measure of  7=? 68 112 68 112 112 112 7 68

34. Measure of  7=? 68 112 68 112 112 112 68 68

35. You just found 7 angle measures when you were given only one angle measure!

36. You know that if two lines are parallel, then the transversal will form congruent alternate interior angles. m 59 59 n

37. Do you think line m is parallel to line n? Why? m 59 59 n