8-3 Angle Relationships Warm Up Problem of the Day Lesson Presentation Course 2 Warm Up Problem of the Day Lesson Presentation

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

8-3 Angle Relationships Problem of the Day Course 2 8-3 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

Course 2 8-3 Angle Relationships Learn to identify parallel, perpendicular, and skew lines, and angles formed by a transversal.

Insert Lesson Title Here Course 2 8-3 Angle Relationships Insert Lesson Title Here Vocabulary perpendicular lines parallel lines skew lines adjacent angles vertical angles transversal corresponding angles

Course 2 8-3 Angle Relationships 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 8-3 Angle Relationships The symbol means “is parallel to.” The symbol means “is perpendicular to.” Reading Math

Course 2 8-3 Angle Relationships Additional Example 1A: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. UV and YV The lines appear to intersect to form right angles. UV  YV

Course 2 8-3 Angle Relationships Additional Example 1B: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. XU and WZ The lines are in different planes and do not intersect. XU and WZ are skew.

Course 2 8-3 Angle Relationships Additional Example 1C: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. XY and WZ The lines are in the same plane and do not intersect. XY || WZ

8-3 Angle Relationships Check It Out: Example 1A Course 2 8-3 Angle Relationships Check It Out: Example 1A Tell whether the lines appear parallel, perpendicular, or skew. WX and XU WX  XU The lines appear to intersect to form right angles.

8-3 Angle Relationships Check It Out: Example 1B Course 2 8-3 Angle Relationships Check It Out: Example 1B Tell whether the lines appear parallel, perpendicular, or skew. WX and UV The lines are in different planes and do not intersect. WX and UV are skew

8-3 Angle Relationships Check It Out: Example 1C Course 2 8-3 Angle Relationships Check It Out: Example 1C Tell whether the lines appear parallel, perpendicular, or skew. WX and ZY The lines are in the same plane and do not intersect. WX || ZY

Course 2 8-3 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.

8-3 Angle Relationships Reading Math Course 2 8-3 Angle Relationships Reading Math Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.

Course 2 8-3 Angle Relationships 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 8-3 Angle Relationships 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°.

Course 2 8-3 Angle Relationships Additional Example 2B: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. 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 8-3 Angle Relationships Additional Example 2C: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. 4 4 is an obtuse angle. Since all of the obtuse angles in the figure are congruent, m4 = 130°.

8-3 Angle Relationships Check It Out: Example 2A Course 2 8-3 Angle Relationships 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°.

8-3 Angle Relationships Check It Out: Example 2B Course 2 8-3 Angle Relationships 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 obtuse angles. Since vertical angles are congruent, m6 = 135°.

8-3 Angle Relationships Check It Out: Example 2C Course 2 8-3 Angle Relationships 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 4 is an obtuse angle. m4 + 45° = 180° In the figure, the acute and obtuse angles are supplementary. –45° –45° Subtract 45° to isolate m4. m4 = 135°

Insert Lesson Title Here Course 2 8-3 Angle Relationships Insert Lesson Title Here 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 5. Find the measure of 4, 5, and 6. 55°, 125°, 125°