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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. Math Journal (5 Min).

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Warm Up

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  1. Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

  2. 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. Homework Review (5 Min)

  4. Warm Up Find the complement of each angle measure. 1. 30° 2. 42° 60° 48° Find the supplement of each angle measure. 4. 82° 98° 3. 150° 30°

  5. 3; AB, AC, BC 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.

  6. Textbook Examples (I Do) (5 Min)

  7. Learn to identify parallel, perpendicular, and skew lines, and angles formed by a transversal.

  8. Vocabulary perpendicular lines parallel lines skew lines adjacent angles vertical angles transversal

  9. 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. Reading Math The symbol means “is parallel to.” The symbol means “is perpendicular to.”

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

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

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

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

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

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

  17. 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. 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

  18. Reading Math Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.

  19. A transversalis a line that intersects two or more lines. Transversals to parallel lines form special angle pairs.

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

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

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

  23. Check It Out: Example 2A Line n line p. Find the measure of the angle. 45° 4 5 6 2 3 135° 7 n p 3 3 and the 45° angle are vertical angles. Since vertical angles are congruent, m3 = 45°.

  24. Check It Out: Example 2B Line n line p. Find the measure of the angle. 45° 4 5 6 2 3 135° 7 n p 6 6 and the 135° angle are vertical angles. m6 = 135°.

  25. Check It Out: Example 2C Line n line p. Find the measure of the angle. 45° 4 5 6 2 3 135° 7 4 n p Adjacent angles formed by two intersecting lines are supplementary. m4 + 45° = 180° Subtract 45° to isolate m4. –45° –45° m4 = 135°

  26. Class work Problems (We Do) (10 Min) • Pg. 324-325 (1-6)

  27. Small Group CW(Yall Do) (10 Min) • Pg. 324-325 (8-26 EOE)

  28. Homework (You Do) (10 Min) • Pg. 324-325 (9, 11, 15, 17, 21 odd)

  29. 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.

  30. Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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

  32. Lesson Quiz for Student Response Systems • 1. Use the figure to identify the type of the given lines. A. parallel B. perpendicular C. skew D. none

  33. Lesson Quiz for Student Response Systems • 2. Use the figure to identify the type of the given lines. A. parallel B. perpendicular C. skew D. none

  34. Lesson Quiz for Student Response Systems • 3. Use the figure to identify the type of the given lines. A. parallel B. perpendicular C. skew D. none

  35. Lesson Quiz for Student Response Systems • 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°

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