7-3 parallel and perpendicular lines - kyrene school district...tell whether the lines appear...
TRANSCRIPT
Learn to identify parallel, perpendicular, and skew lines, and angles formed by a
transversal.
Course 2
7-3 Parallel and Perpendicular Lines
Vocabulary
perpendicular lines
parallel lines
skew lines
vertical angles
transversal
Insert Lesson Title Here
Course 2
7-3 Parallel and Perpendicular Lines
Course 2
7-3 Parallel and Perpendicular Lines
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
7-3 Parallel and Perpendicular Lines
The symbol means “is parallel to.” The symbol means “is perpendicular to.”
Reading Math
Tell whether the lines appear parallel, perpendicular, or skew.
Additional Example 1A: Identifying Parallel,
Perpendicular, and Skew Lines
Course 2
7-3 Parallel and Perpendicular Lines
A. UV and YVThe lines appear to intersect to form right angles.UV YV
X Y
V
ZW
U
Tell whether the lines appear parallel, perpendicular, or skew.
Additional Example 1B: Identifying Parallel,
Perpendicular, and Skew Lines
Course 2
7-3 Parallel and Perpendicular Lines
B. XU and WZ
The lines are in different planes and do not intersect.
XU and WZ are skew.
X Y
V
ZW
U
Tell whether the lines appear parallel, perpendicular, or skew.
Additional Example 1C: Identifying Parallel,
Perpendicular, and Skew Lines
Course 2
7-3 Parallel and Perpendicular Lines
C. XY and WZ
The lines are in the same plane and do not intersect.
XY || WZ
X Y
V
ZW
U
Tell whether the lines appear parallel, perpendicular, or skew.
Try This: Example 1A
Course 2
7-3 Parallel and Perpendicular Lines
A. WX and XU
The lines appear to intersect to form right angles.
WX XU
X Y
V
ZW
U
Tell whether the lines appear parallel, perpendicular, or skew.
Try This: Example 1B
Course 2
7-3 Parallel and Perpendicular Lines
B. WX and UV
The lines are in different planes and do not intersect.
WX and UV are skew
X Y
V
ZW
U
Tell whether the lines appear parallel, perpendicular, or skew.
Try This: Example 1C
Course 2
7-3 Parallel and Perpendicular Lines
C. WX and ZY
The lines are in the same plane and do not intersect.
WX || ZY
X Y
V
ZW
U
Course 2
7-3 Parallel and Perpendicular Lines
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.
Course 2
7-3 Parallel and Perpendicular Lines
A transversal is a line that intersects two or more lines. Eight angles are formed when a transversal intersects two lines. When those two lines are parallel, all of the acute angles formed are congruent, and all of the obtuse angles formed are congruent. These obtuse and acute angles are supplementary.
1 2
3 45 6
7 8
Course 2
7-3 Parallel and Perpendicular Lines
Angles with the same number of tick marks are congruent. The tick marks are placed in the arcs drawn inside the angles.
Reading Math
Line n line p. Find the measure of the angle.
Additional Example 2A: Using Angle Relationships to
Find Angle Measures
Course 2
7-3 Parallel and Perpendicular Lines
A. 2
2 and the 130° angle are vertical angles. Since vertical angles are congruent, m 2 = 130°.
Line n line p. Find the measure of the angle.
Additional Example 2B: Using Angle Relationships to
Find Angle Measures
Course 2
7-3 Parallel and Perpendicular Lines
B. 3
3 and the 50° angle are acute angles. Since all of the acute angles in the figure are congruent, m 3 = 50°.
Line n line p. Find the measure of the angle.
Additional Example 2C: Using Angle Relationships to
Find Angle Measures
Course 2
7-3 Parallel and Perpendicular Lines
C. 4
4 is an obtuse angle. Since all of the obtuse angles in the figure are congruent, m 4 = 130°.
Line n line p. Find the measure of the angle.
Try This: Example 2A
Course 2
7-3 Parallel and Perpendicular Lines
A. 3
3 and the 45° angle are vertical angles. Since vertical angles are congruent, m 3 = 45°.
45°
2 3 135°5 64
7
n p
Line n line p. Find the measure of the angle.
Try This: Example 2B
Course 2
7-3 Parallel and Perpendicular Lines
B. 6
6 and the 135° angle are obtuse angles. Since vertical angles are congruent, m 6 = 135°.
45°
2 3 135°5 64
7
n p
Line n line p. Find the measure of the angle.
Try This: Example 2C
Course 2
7-3 Parallel and Perpendicular Lines
C. 4
4 is an obtuse angle. m 4 + 45° = 180°
–45° –45°
m 4 = 135°
In the figure, the acute and obtuse angles are supplementary.
Subtract 45° to isolate m 4.
45°
2 3 135°5 64
7
n p
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
Insert Lesson Title Here
skew
Both are always the same distance apart, but railroad tracks are not always straight.
Course 2
7-3 Parallel and Perpendicular Lines
How are railroad tracks and two parallel lines alike, and how are they different?
D
Homework7-3 Worksheet