1. 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

2. 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.

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

4. 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

5. 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.

6. 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

7. 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. 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

9. 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

10. 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.

11. 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.

12. 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.

13. 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°.

14. 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°.

15. 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°.

16. 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°.

17. 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°.

18. 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°

19. 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°