1. 8-3 Line and Angle Relationships Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 8-3 Line and Angle Relationships Math Journal (5 Min) 3-2-1 - Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write 3 statements that they already know about the lesson being presented, 2 questions that they have before the lesson is presented, and 1 connection that they feel can be made between what they already know and what they think they will be taught in the new lesson before they have been taught the lesson, and at the end of class, write 3 statements that they now know about the lesson being presented, answer the 2 questions that they had written previously, and 1 connection that they now know can be made between what they knew before the lesson and what they now know after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 statement or connection that pertained to the lesson.

3. 8-3 Line and Angle Relationships Homework Review (5 Min)

4. 8-3 Line and Angle Relationships Warm Up Find the complement of each angle measure. 1. 30° 2. 42° 60° 48° 30° 3. 150° Find the supplement of each angle measure. 4. 82°98°

5. 8-3 Line and Angle Relationships Problem of the Day Draw three points that are not on the same line. Label them A, B, and C. How many lines can you draw that are determined by the points? Name the lines. 3; AB, AC, BC

6. 8-3 Line and Angle Relationships Textbook Examples (I Do) (5 Min)

7. 8-3 Line and Angle Relationships Learn to identify parallel, perpendicular, and skew lines, and angles formed by a transversal.

8. 8-3 Line and Angle Relationships Vocabulary perpendicular lines parallel lines skew lines adjacent angles vertical angles transversal

9. 8-3 Line and Angle Relationships When lines, segments, or rays intersect, they form angles. If the angles formed by two intersecting lines measure 90°, the lines are perpendicular lines. Some lines in the same plane do not intersect at all. These lines are parallel lines. Segments and rays that are part of parallel lines are also parallel. Skew lines do not intersect, and yet they are also not parallel. They lie in different planes.

10. 8-3 Line and Angle Relationships The symbol means “is parallel to.” The symbol means “is perpendicular to.” Reading Math

11. 8-3 Line and Angle Relationships Tell whether the lines appear parallel, perpendicular, or skew. Additional Example 1A: Identifying Parallel, Perpendicular, and Skew Lines The lines appear to intersect to form right angles. UV and YV UV  YV 8-3

12. Line and Angle Relationships Tell whether the lines appear parallel, perpendicular, or skew. Additional Example 1B: Identifying Parallel, Perpendicular, and Skew Lines The lines are in different planes and do not intersect. XU and WZ are skew.

13. 8-3 Line and Angle Relationships Tell whether the lines appear parallel, perpendicular, or skew. Additional Example 1C: Identifying Parallel, Perpendicular, and Skew Lines The lines are in the same plane and do not intersect. XY and WZ XY || WZ

14. 8-3 Line and Angle Relationships Tell whether the lines appear parallel, perpendicular, or skew. Check It Out: Example 1A The lines appear to intersect to form right angles. WX and XU WX  XU

15. 8-3 Line and Angle Relationships Tell whether the lines appear parallel, perpendicular, or skew. Check It Out: Example 1B The lines are in different planes and do not intersect. WX and UV are skew.

16. 8-3 Line and Angle Relationships Tell whether the lines appear parallel, perpendicular, or skew. Check It Out: Example 1C The lines are in the same plane and do not intersect. WX and ZY WX || ZY

17. 8-3 Line and Angle Relationships Adjacent angles have a common vertex and a common side, but no common interior points. Angles 2 and 3 in the diagram are adjacent. Adjacent angles formed by two intersecting lines are supplementary Vertical angles are the opposite angles formed by two intersecting lines. Angles 1 and 3 in the diagram are vertical angles. Vertical angles have the same measure, so they are congruent.

18. 8-3 Line and Angle Relationships Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles. Reading Math

19. 8-3 Line and Angle Relationships A transversal is a line that intersects two or more lines. Transversals to parallel lines form special angle pairs.

20. 8-3 Line and Angle Relationships

21. 8-3 Line and Angle Relationships Line n line p. Find the measure of the angle. Additional Example 2A: Using Angle Relationships to Find Angle Measures 22 2 and the 130° angle are vertical angles. Since vertical angles are congruent, m2 = 130°.

22. 8-3 Line and Angle Relationships Line n line p. Find the measure of the angle. Additional Example 2B: Using Angle Relationships to Find Angle Measures 33 m3 + 130° = 180° –130° m  3 = 50° Adjacent angles formed by two intersecting lines are supplementary. Subtract 130° to isolate m3.

23. 8-3 Line and Angle Relationships Line n line p. Find the measure of the angle. Additional Example 2C: Using Angle Relationships to Find Angle Measures 44 Alternate interior angles are congruent. m4 = 130°.

24. 8-3 Line and Angle Relationships Line n line p. Find the measure of the angle. Check It Out: Example 2A 33 3 and the 45° angle are vertical angles. Since vertical angles are congruent, m3 = 45°. 45° 2 3135° 56 4 7 np

25. 8-3 Line and Angle Relationships Line n line p. Find the measure of the angle. Check It Out: Example 2B 66 6 and the 135° angle are vertical angles. m6 = 135°. 45° 2 3135° 56 4 7 np

26. 8-3 Line and Angle Relationships Line n line p. Find the measure of the angle. Check It Out: Example 2C 44 m4 + 45° = 180° –45° m  4 = 135° Adjacent angles formed by two intersecting lines are supplementary. Subtract 45° to isolate m4. 45° 2 3135° 56 4 7 np

27. 8-3 Line and Angle Relationships Class work Problems (We Do) (10 Min) Pg. 324-325 (1-6)

28. 8-3 Line and Angle Relationships

29. 8-3 Line and Angle Relationships Small Group CW(Yall Do) (10 Min) Pg. 324-325 (8-26 EOE)

30. 8-3 Line and Angle Relationships

31. 8-3 Line and Angle Relationships

32. 8-3 Line and Angle Relationships

33. 8-3 Line and Angle Relationships Homework (You Do) (10 Min) Pg. 324-325 (9, 11, 15, 17, 21 odd)

34. 8-3 Line and Angle Relationships Math Journal (5 Min) 3-2-1 - Each student will be given the title of the lesson that will be taught that day. They must then, at the beginning of class, write 3 statements that they already know about the lesson being presented, 2 questions that they have before the lesson is presented, and 1 connection that they feel can be made between what they already know and what they think they will be taught in the new lesson before they have been taught the lesson, and at the end of class, write 3 statements that they now know about the lesson being presented, answer the 2 questions that they had written previously, and 1 connection that they now know can be made between what they knew before the lesson and what they now know after they have been taught the lesson. Then, each student will discuss his/her answers within their group. Finally, to leave class, each student will have to give/write 1 statement or connection that pertained to the lesson.

35. 8-3 Line and Angle Relationships Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

36. 8-3 Line and Angle Relationships Lesson Quiz Tell whether the lines appear parallel, perpendicular, or skew. 1. AB and CD 2. EF and FH 3. AB and CG 4. perpendicular parallel skew 55°, 125°, 125° In Exercise 28, line r || line s. Find the measures of 4, 5, and 7.

37. 8-3 Line and Angle Relationships 1. Use the figure to identify the type of the given lines. A. parallel B. perpendicular C. skew D. none Lesson Quiz for Student Response Systems

38. 8-3 Line and Angle Relationships 2. Use the figure to identify the type of the given lines. A. parallel B. perpendicular C. skew D. none Lesson Quiz for Student Response Systems

39. 8-3 Line and Angle Relationships 3. Use the figure to identify the type of the given lines. A. parallel B. perpendicular C. skew D. none Lesson Quiz for Student Response Systems

40. 8-3 Line and Angle Relationships 4. In the figure, line x || line y. Identify the measures of 2, 6, and 7. A. 70°, 110°, 70° B. 110°, 70°, 70° C. 110°, 110°, 70° D. 70°, 70°, 110° Lesson Quiz for Student Response Systems