This document discusses properties of parallel lines cut by a transversal. It defines key terms like parallel lines, transversal, corresponding angles, alternate interior angles, and alternate exterior angles. It then presents conjectures that corresponding angles, alternate interior angles, and alternate exterior angles are congruent when two parallel lines are cut by a transversal. Examples are given to illustrate these properties and how determining the measure of one angle allows calculating the measures of all other angles formed.

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