Transcript 8-3
8-3 Line and Angle Relationships Warm Up Find the complement of each angle measure. 1. 30° 60° 2. 42° 48° Find the supplement of each angle measure. 3. 150° 30° 4. 82° 98° 8-3 Line and Angle Relationships Intersecting lines are lines that cross at one common point. W Y Z X YZ intersects WX. B Parallel lines are lines in the same plane that never intersect. Reading Math A Line YZ intersects line WX. L Line AB is parallel to line ML. AB ML. M The red arrows on the lines show that the lines are parallel. 8-3 Line and Angle Relationships Perpendicular lines intersect to form 90° angles, T or right angles. Skew lines are lines that lie in different planes. They are neither parallel nor intersecting. M L R U Line RS is perpendicular to line TU. RS S B A TU. Line AB and line ML are skew. AB and ML are skew. 8-3 Line and Angle Relationships Example 1A: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. UV and YV UV YV The lines appear to intersect to form right angles. 8-3 Line and Angle Relationships Example 1B: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. XU and WZ XU and WZ are skew. The lines are in different planes and do not intersect. 8-3 Line and Angle Relationships Example 1C: Identifying Parallel, Perpendicular, and Skew Lines Tell whether the lines appear parallel, perpendicular, or skew. XY and WZ XY || WZ The lines are in the same plane and do not intersect. 8-3 Line and 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 Line and Angle Relationships Check It Out: Example 1B Tell whether the lines appear parallel, perpendicular, or skew. WX and UV WX and UV are skew. The lines are in different planes and do not intersect. 8-3 Line and Angle Relationships Check It Out: Example 1C Tell whether the lines appear parallel, perpendicular, or skew. WX and ZY WX || ZY The lines are in the same plane and do not intersect. 8-3 Line and 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. Angles 1 and 3 in the diagram are vertical angles. Vertical angles have the same measure, so they are congruent. 8-3 Line and 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. 8-3 Line and Angle Relationships A transversal is a line that intersects two or more lines. Transversals to parallel lines form special angle pairs. 8-3 Line and Angle Relationships 8-3 Line and Angle Relationships 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, m2 = 130°. 8-3 Line and Angle Relationships Example 2B: Using Angle Relationships to Find Angle Measures Line n line p. Find the measure of the angle. 3 m3 + 130° = 180° –130° –130° m3 = 50° Adjacent angles formed by two intersecting lines are supplementary. Subtract 130° to isolate m3. 8-3 Line and Angle Relationships 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. m4 = 130°. 8-3 Line and 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 3 n p 3 and the 45° angle are vertical angles. Since vertical angles are congruent, m3 = 45°. 8-3 Line and 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 6 n p 6 and the 135° angle are vertical angles. m6 = 135°. 8-3 Line and 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 Adjacent angles formed by two m4 + 45° = 180° intersecting lines are supplementary. –45° –45° m4 = 135° Subtract 45° to isolate m4. 8-3 Line and Angle Relationships Lesson Quiz Tell whether the lines appear parallel, perpendicular, or skew. 1. AB and CD parallel 2. EF and FH perpendicular 3. AB and CG skew 4. In Exercise 28, line r || line s. Find the measures of 4, 5, and 7. 55°, 125°, 125°