8-3 Line and Angle Relationships

Warm UpFind the complement of each angle measure.

1. 30° 2. 42°60° 48°

30°3. 150°

Find the supplement of each angle measure.

4. 82° 98°

8-3 Line and Angle Relationships

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

8-3 Line and Angle Relationships

When lines, segments, or rays intersect, they form angles. If the angles formed by two intersecting lines measure 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.

8-3 Line and Angle Relationships

The symbol means “is parallel to.” The symbol means “is perpendicular to.”

Reading Math

8-3 Line and 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

8-3

8-3 Line and 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.

8-3 Line and 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

8-3 Line and Angle Relationships

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 XUWX XU

8-3 Line and Angle Relationships

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

WX and UV are skew.

8-3 Line and Angle Relationships

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

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 supplementaryVertical 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

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

Reading Math

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

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°.

8-3 Line and Angle Relationships

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

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

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

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

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

4

Alternate interior angles are congruent. m4 = 130°.

8-3 Line and Angle Relationships

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

Check It Out: Example 2A

3

3 and the 45° angle are vertical angles. Since vertical angles are congruent, m3 = 45°.

45°2 3 135°

5 647

n p

8-3 Line and Angle Relationships

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

Check It Out: Example 2B

6

6 and the 135° angle are vertical angles.m6 = 135°.

45°2 3 135°

5 647

n p

8-3 Line and Angle Relationships

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

Check It Out: Example 2C

4

m4 + 45° = 180°

–45° –45°

m4 = 135°

Adjacent angles formed by two intersecting lines are supplementary.

Subtract 45° to isolate m4.

45°2 3 135°

5 647

n p

8-3 Line and 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

skew

55°, 125°, 125°

In Exercise 28, line r || line s. Find the measures of 4, 5, and 7.