1. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Tell whether the lines appear parallel, perpendicular, or skew. 1. AB and CD 2. EF and FH 3. AB and CG What are we doing today?

2. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Warm Up Find the complement of each angle measure. 1. 30° 2. 42° 3. 150° Find the supplement of each angle measure. 4. 82°

3. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. 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°

4. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. I will… Learn to identify parallel, perpendicular, and skew lines, and angles formed by a transversal.

5. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Vocabulary perpendicular lines parallel lines skew lines adjacent angles vertical angles transversal

6. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. 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. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. The symbol means “is parallel to.” The symbol means “is perpendicular to.” Reading Math

8. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Tell whether the lines appear parallel, perpendicular, or skew. Example 1: Identifying Parallel, Perpendicular, and Skew Lines UV and YV 8-3 1a. 1b. XU and WZ XY and WZ 1c.

9. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Tell whether the lines appear parallel, perpendicular, or skew. Example 1a – WORKED OUT The lines appear to intersect to form right angles. UV and YV UV  YV 8-3

10. I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Tell whether the lines appear parallel, perpendicular, or skew. Example 1b - WORKED OUT The lines are in different planes and do not intersect. XU and WZ are skew.

11. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Tell whether the lines appear parallel, perpendicular, or skew. Example 1c - WORKED OUT The lines are in the same plane and do not intersect. XY and WZ XY || WZ

12. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Tell whether the lines appear parallel, perpendicular, or skew. WX and XU PRACTICE 1 1a. 1b. 1c. WX and UV WX and ZY

13. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Tell whether the lines appear parallel, perpendicular, or skew. The lines appear to intersect to form right angles. WX and XU WX  XU PRACTICE 1a – Worked Out

14. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Tell whether the lines appear parallel, perpendicular, or skew. The lines are in different planes and do not intersect. WX and UV are skew. PRACTICE 1b – Worked Out

15. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Tell whether the lines appear parallel, perpendicular, or skew. The lines are in the same plane and do not intersect. WX and ZY WX || ZY PRACTICE 1c – Worked Out

16. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. 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

17. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. 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 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. 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 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. A transversal is a line that intersects two or more lines. Transversals to parallel lines form special angle pairs.

20. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal.

21. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Example 2: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. 22 2a. 2b. 2c. 33 44

22. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Example 2a – WORKED OUT Line n line p. Find the measure of the angle. 22 2 and the 130° angle are vertical angles. Since vertical angles are congruent, m2 = 130°.

23. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Example 2b – WORKED OUT Line n line p. Find the measure of the angle. 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.

24. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Example 2c – WORKED OUT 44 Alternate interior angles are congruent. m4 = 130°. Line n line p. Find the measure of the angle.

25. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Line n line p. Find the measure of the angle. PRACTICE 2 45° 2 3135° 56 4 7 np 33 2a. 2b. 2c. 66 44

26. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Line n line p. Find the measure of the angle. 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 PRACTICE 2a – Worked Out

27. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Line n line p. Find the measure of the angle. 66 45° 2 3135° 56 4 7 np PRACTICE 2b – Worked Out 6 and the 135° angle are vertical angles. m6 = 135°.

28. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Line n line p. Find the measure of the angle. 44 45° 2 3135° 56 4 7 np PRACTICE 2c – Worked Out m4 + 45° = 180° –45° m  4 = 135° Adjacent angles formed by two intersecting lines are supplementary. Subtract 45° to isolate m4.

29. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Lesson Quiz What did YOU learn today?

30. 8-3 I WILL... identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Tell whether the lines appear parallel, perpendicular, or skew. 1. AB and CD 2. EF and FH 3. AB and CG perpendicular parallel skew