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°

Intersecting lines are lines that cross at one common point. Y W Z X Intersecting lines are lines that cross at one common point. Line YZ intersects line WX. YZ intersects WX. B A M L Parallel lines are lines in the same plane that never intersect. Line AB is parallel to line ML. AB ML. The red arrows on the lines show that the lines are parallel. Reading Math

Perpendicular lines intersect to form 90° angles, or right angles. Line RS is perpendicular to line TU. RS TU. Skew lines are lines that lie in different planes. They are neither parallel nor intersecting. Line AB and line ML are skew. AB and ML are skew. M L A B 3

Example 1A: Identifying Parallel, Perpendicular, and Skew Lines 8-3 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

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.

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

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.

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.

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

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.

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

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

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°.

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°

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°.

Line n line p. Find the measure of the angle. 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°.

Line n line p. Find the measure of the angle. 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°.

Line n line p. Find the measure of the angle. 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° –45° –45° Subtract 45° to isolate m4. m4 = 135°

Tell whether the lines appear parallel, perpendicular, or skew. 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° 20