Warm- Up

1. How to identify pairs of lines and special angles formed by two lines and a transversal? Warm- Up Draw and define each (know slope of parallel and perpendicular lines). Parallel Lines- Perpendicular Lines- Skew Lines-

2. How to identify pairs of lines and special angles formed by two lines and a transversal? Lines p. 146 • Parallel lines have the __________ slope. • Perpendicular lines form _______ angles. • Skew lines do not ________ and are not in the __________. • * Draw a rectangular prism* • Steps: • Draw two figures to represent the top and bottom of the prism. • Draw the vertical edges. • Make the hidden edges of the prism dashed. • Label the vertices of the prism. • Draw a rectangular prism • Complete the following questions D A G K E B F C

3. How to identify pairs of lines and special angles formed by two lines and a transversal? Parallel Lines Cut By aTransversal

4. How to identify pairs of lines and special angles formed by two lines and a transversal? Parallel Lines • Never intersect • Equal distance apart; equidistant • Symbol || • Have the same slope

5. How to identify pairs of lines and special angles formed by two lines and a transversal? Perpendicular Lines • Form 4 right angles • Have opposite reciprocal slopes • Symbol|

6. How to identify pairs of lines and special angles formed by two lines and a transversal? Parallel Lines Cut by a Transversal When parallel lines are given in a figure, there are two main areas: the interior and the exterior. 

7. How to identify pairs of lines and special angles formed by two lines and a transversal? Transversal • A line that intersect two or more lines • Form special angles • 8 angles are formed when parallel lines are cut by a transversal

8. How to identify pairs of lines and special angles formed by two lines and a transversal? Think About It Exterior Exterior Interior Interior Exterior Exterior

9. How to identify pairs of lines and special angles formed by two lines and a transversal? Alternate Interior Angles • Two angles that lie between the two lines on opposite sides of the transversal • Angle measures are CONGRUENT • Alternate: opposite • Interior: inside

10. How to identify pairs of lines and special angles formed by two lines and a transversal? Alternate Exterior Angles • Two angles that lie outside the two lines on opposite sides of the transversal • Angle measures are CONGRUENT • Alternate: opposite • Exterior: outside

11. How to identify pairs of lines and special angles formed by two lines and a transversal? Corresponding Angles • Two angles that occupy corresponding position • Angle measures are CONGRUENT • Corresponding: same

12. How to identify pairs of lines and special angles formed by two lines and a transversal? Vertical Angles • Angles formed by intersecting lines • Angle measures are CONGRUENT

13. How to identify pairs of lines and special angles formed by two lines and a transversal? LINEar Pair • Two adjacent angles that form a line • Angles measures are SUPPLEMENTARY- 180 degrees

14. How to identify pairs of lines and special angles formed by two lines and a transversal? Consecutive Interior Angles • AKA: Same-side interior angles • Two angles that lie between the two lines on the same side of the transversal • Angles measures are SUPPLEMENTARY- 180 degrees

15. How to identify pairs of lines and special angles formed by two lines and a transversal? Summarize • What does it mean if two parallel lines are cut by a transversal? • Answer: The above six pairs of special angles are formed; angles that are congruent and/ or supplementary

16. How to identify pairs of lines and special angles formed by two lines and a transversal? Practice • p. 148 • Think and Discuss • # 1- 13

17. Warm-Up Part 1:Name two pairs of each angles • Alternate Interior • Alternate Exterior • Corresponding • Consecutive Interior

18. Warm-Up Part 2:Identify types of lines and planes • Two pairs of parallel segments • Two pairs of perpendicular segments • A pair of skew segments • A pairs of parallel planes

19. Check Practice • 3.1 Objective: • Identify parallel, perpendicular, and skew lines • Identify the angles formed by two lines and a transversal • P. 148 • # 1- 13 • Think and Discuss

20. Practice Review Vocabulary

21. Transversal

22. Alternate

23. Interior

24. Exterior

25. Corresponding

26. Consecutive

27. Vertical

28. Practice Determine if the pair of angles are CONGRUENT or SUPPLEMENTARY Explain.

29. Move to the… LeftMiddleRight Supplementary BOTH Congruent

30. Red Dots

32. < 6 & < 8

33. < a & < d

34. < 1 & < 2

35. < 1 & < 3

36. < G & < H

38. < e & < g

39. < a & < h

40. < 1 & < 2

41. < 3 & < 5

42. Orange circles

43. Parallel Lines Project • Objective: • Students will demonstrate their knowledge of parallel lines with a transversal. • Students will show when angles are congruent or supplementary given parallel lines and a transversal • Materials: • Pencil • Colored pencils or markers • Ruler • Paper (graph paper, if desired) • Overview: • For this project, each student will make his or her own street map for a fictional city.

44. Warm-Up:Find the missing measure. • If the m < 5 = 120, find m < 4. ________ • If the m < 3 = 72, find m < 8. ________ • If the m < 7 = 91, find m < 1. ________ • If the m < 6 = 73, find m < 2. ________

47. 126º Xº

48. Which measurement is incorrect?Fill in the other measurements.

49. 3.2 Angles Formed by Parallel Lines and transversal Objective: Prove and use theorems about the angles formed by parallel lines and a transversal.

50. Question When parallel lines are cut by a transversal, the angle pairs formed are either _______or ______.