1. 7-3 Angle Relationships Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Find the complement of each angle measure. 1. 30° 2. 42° 60° 48° 30° Course 2 7-3 Angle Relationships 3. 150° Find the supplement of each angle measure. 4. 82°98°

3. 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 Course 2 7-3 Angle Relationships

4. Learn to identify parallel, perpendicular, and skew lines, and angles formed by a transversal. Course 2 7-3 Angle Relationships

5. Vocabulary perpendicular lines parallel lines skew lines adjacent angles vertical angles transversal corresponding angles Insert Lesson Title Here Course 2 7-3 Angle Relationships

6. When lines, segments, or rays intersect, they form angles. If the angles formed by two intersecting lines are equal to 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. Course 2 7-3 Angle Relationships

7. The symbol means “is parallel to.” The symbol means “is perpendicular to.” Reading Math Course 2 7-3 Angle Relationships

8. 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 Course 2 7-3 Angle Relationships

9. 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. Course 2 7-3 Angle Relationships

10. 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 Course 2 7-3 Angle Relationships

11. 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 Course 2 7-3 Angle Relationships

12. 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 Course 2 7-3 Angle Relationships

13. 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 Course 2 7-3 Angle Relationships

14. Course 2 7-3 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. When two lines intersect, two pairs of vertical angles are formed. Vertical angles have the same measure, so they are congruent.

15. Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles. Reading Math Course 2 7-3 Angle Relationships

16. A transversal is a line that intersects two or more lines. Line t is a transversal. When the lines that are intersected are parallel, four pairs of corresponding angles are formed. Corresponding angles are on the same side of the transversal and are both above or both below the parallel lines. Angles 1 and 5 are corresponding angles. Corresponding angles are congruent. Course 2 7-3 Angle Relationships

17. 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°. Course 2 7-3 Angle Relationships

18. Line n line p. Find the measure of the angle. Additional Example 2B: Using Angle Relationships to Find Angle Measures 33 3 and the 50° angle are acute angles. Since all of the acute angles in the figure are congruent, m3 = 50°. Course 2 7-3 Angle Relationships

19. Line n line p. Find the measure of the angle. Additional Example 2C: Using Angle Relationships to Find Angle Measures 44 4 is an obtuse angle. Since all of the obtuse angles in the figure are congruent, m4 = 130°. Course 2 7-3 Angle Relationships

20. 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 Course 2 7-3 Angle Relationships

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

22. Line n line p. Find the measure of the angle. Check It Out: Example 2C 44 4 is an obtuse angle. m4 + 45° = 180° –45° m  4 = 135° In the figure, the acute and obtuse angles are supplementary. Subtract 45° to isolate m4. 45° 2 3135° 56 4 7 np Course 2 7-3 Angle Relationships

23. 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 Insert Lesson Title Here skew 55°, 125°, 125° In Exercise 28, line r line 5. Find the measure of 4, 5, and 6. Course 2 7-3 Angle Relationships