Warm UpFind the complement of each angle measure.

1. 30° 2. 42°60° 48°

30°

Course 2

8-3 Angle Relationships

3. 150°

Find the supplement of each angle measure.

4. 82° 98°

Learn to identify parallel, perpendicular, and skew lines, and angles formed by a transversal.

Course 2

8-3 Angle Relationships

Vocabulary

perpendicular linesparallel linesskew linesadjacent anglesvertical anglestransversalcorresponding angles

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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

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

8-3 Angle Relationships

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

XU and WZ are skew.

Course 2

8-3 Angle Relationships

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

8-3 Angle Relationships

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 supplementaryVertical 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.

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

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

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

Additional Example 2A: Using Angle Relationships to Find Angle Measures

22 and the 130° angle are vertical angles. Since vertical angles are congruent, m2 = 130°.

Course 2

8-3 Angle Relationships

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

Additional Example 2B: Using Angle Relationships to Find Angle Measures

33 and the 50° angle are acute angles. Since all of the acute angles in the figure are congruent, m3 = 50°.

Course 2

8-3 Angle Relationships

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

Additional Example 2C: Using Angle Relationships to Find Angle Measures

4

4 is an obtuse angle. Since all of the obtuse angles in the figure are congruent, m4 = 130°.

Course 2

8-3 Angle Relationships

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

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skew

55°, 125°, 125°

In Exercise 28, line r line 5. Find the measure of 4, 5, and 6.

Course 2

8-3 Angle Relationships