7-3 Parallel and Perpendicular Lines
Learn to identify parallel, perpendicular,
and skew lines, and angles formed by a
transversal.
Course 2
7-3 Parallel
Insert Lesson
Title Here Lines
and Perpendicular
Vocabulary
perpendicular lines
parallel lines
intersecting lines
skew lines
vertical angles
complimentary angles
supplementary angles
transversal
Course 2
7-3 Angle Relationships
Complementary angles are two angles
whose measures have a sum of 90°.
65° + 25° = 90°
LMN and
NMP are complementary.
L
N
65°
25°
M
Course 1
P
7-3 Angle Relationships
Supplementary angles are two angles whose
measures have a sum of 180°.
65° + 115° = 180°
GHK and
KHJ are supplementary.
K
65°
G
Course 1
115°
H
J
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.
R
T
U
S
Line RS is
perpendicular
to line TU.
RS
TU.
Writing Math
The square inside a right angle shows that
the rays of the angle are perpendicular.
Course 2
7-3 Parallel and 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.
B
A
L
Line AB is
parallel to line
ML.
AB
M
Course 2
ML.
7-3 Parallel and Perpendicular Lines
Skew lines do not intersect, and yet they
are also not parallel. They lie in different
planes.
M
L
Course 2
B
A
Line AB and
line ML are
skew.
AB and ML are
skew.
7-3 Parallel and Perpendicular Lines
Intersecting Lines lines that cross at one
common point.
W
Y
Z
Course 2
X
Line YZ
intersects line
WX.
YZ intersects
WX.
7-3 Parallel and Perpendicular Lines
Reading Math
The symbol means “is parallel to.” The
symbol means “is perpendicular to.”
Course 2
7-3 Parallel and Perpendicular Lines
Additional Example 1A: Identifying Parallel,
Perpendicular, and Skew Lines
Tell whether the lines appear parallel,
perpendicular, or skew.
X
Y
V
U
W
A. UV and YV
UV  YV
Course 2
Z
The lines appear to intersect
to form right angles.
7-3 Parallel and Perpendicular Lines
Additional Example 1B: Identifying Parallel,
Perpendicular, and Skew Lines
Tell whether the lines appear parallel,
perpendicular, or skew.
X
Y
V
U
W
Z
B. XU and WZ
XU and WZ
are skew.
Course 2
The lines are in different
planes and do not intersect.
7-3 Parallel and Perpendicular Lines
Additional Example 1C: Identifying Parallel,
Perpendicular, and Skew Lines
Tell whether the lines appear parallel,
perpendicular, or skew.
X
Y
V
U
W
Z
C. XY and WZ
XY || WZ
Course 2
The lines are in the same
plane and do not intersect.
7-3 Parallel and Perpendicular Lines
When angles have the same measure, they are
said to be congruent.
M
P
160
20°
20° °
R
160
°
N
Q
Vertical angles are formed opposite each other
when two lines intersect. Vertical angles have
the same measure, so they are always
congruent. Kissing angles.
MRP and NRQ are vertical angles.
MRN and
Course 2
PRQ are vertical angles
7-3 Angle Relationships
Adjacent angles are side by side and have a
common vertex and ray. Adjacent angles may or
may not be congruent.
M
P
160
20°
20° °
R
160
°
N
Q
MRN and NRQ are adjacent angles. They
share vertex R and RN.
NRQ and QRP are adjacent angles. They
share vertex R and RQ.
Course 1
7-3 Angle Relationships
Complementary angles are two angles
whose measures have a sum of 90°.
65° + 25° = 90°
LMN and
NMP are complementary.
L
N
65°
25°
M
Course 1
P
7-3 Angle Relationships
Supplementary angles are two angles whose
measures have a sum of 180°.
65° + 115° = 180°
GHK and
KHJ are supplementary.
K
65°
G
Course 1
115°
H
J
7-3 Parallel and Perpendicular Lines
Reading Math
Angles with the same number of tick marks are
congruent. The tick marks are placed in the
arcs drawn inside the angles.
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.
Course 2
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2
3
5
4
7
6
8
7-3 Parallel and Perpendicular Lines
• There are 4 interior angles
• There are 4 exterior angles
Course 2
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2
3
5
4
7
6
8
7-3 Parallel and Perpendicular Lines
• There are 4 pairs of vertical
angles.
• 2 Acute Pairs
• 2 Obtuse Pairs
Course 2
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2
3
5
4
7
6
8
7-3 Parallel and Perpendicular Lines
• There are 4 pairs of
corresponding angles.
1
2
3
5
4
7
Course 2
6
8
7-3 Parallel and Perpendicular Lines
• There are many pairs of
adjacent angles… angles that
share a ray and are therefore
considered to be
supplementary angles.
• 2 blues
• 2 reds
• 1 blue & 1 red
Course 2
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2
3
5
4
7
6
8
7-3 Parallel and Perpendicular Lines
Additional Example 2A: Using Angle Relationships to
Find Angle Measures
Line n
A.
Course 2
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°.
7-3 Parallel and Perpendicular Lines
Additional Example 2B: Using Angle Relationships to
Find Angle Measures
Line n
B.
Course 2
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°.
7-3 Parallel and Perpendicular Lines
Additional Example 2C: Using Angle Relationships to
Find Angle Measures
Line n
C.
Course 2
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°.
7-3 Parallel and Perpendicular Lines
Try This: Example 2A
Line n
line p. Find the measure of the angle.
45° 4
5 6
2 3 135° 7
A.
Course 2
n
p
3
3 and the 45° angle are vertical
angles. Since vertical angles are
congruent, m 3 = 45°.
7-3 Parallel
Insert Lesson
and Perpendicular
Title Here Lines
Lesson Quiz
Tell whether the lines appear
parallel, perpendicular, or skew.
1. AB and CD
parallel
2. EF and FH
perpendicular
3. AB and CG
skew
4. How are railroad tracks and two parallel lines
alike, and how are they different?
Both are always the same distance apart, but
railroad tracks are not always straight.
Course 2
D