Parallel Lines
- 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