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Warm Up

Warm Up. Problem of the Day. Lesson Presentation. Lesson Quizzes. 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°. 3; AB , AC , BC. Problem of the Day

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Warm Up

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

  2. 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°

  3. 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.

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

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

  6. 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.

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

  8. UV and YV UV YV 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.

  9. 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.

  10. 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.

  11. 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.

  12. 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.

  13. 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.

  14. 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

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

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

  17. 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°.

  18. 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°

  19. 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°.

  20. 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°.

  21. 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°.

  22. 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°

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

  24. 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°

  25. 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

  26. 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

  27. 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

  28. 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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