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8-2 Geometric Relationships
Common Core State Standards
Learning Objective
7.G.5
Solve for an unknown angle using
the “properties of angles.”
Holt CA Course 1
8-2 Geometric Relationships
Vocabulary
parallel lines
perpendicular lines
skew lines
parallel planes
perpendicular planes
Holt CA Course 1
8-2 Geometric Relationships
Parallel lines are lines in the same plane
that never intersect.
Line WX is parallel to line YZ.
WX || YZ.
Holt CA Course 1
8-2 Geometric Relationships
Reading Math
The red arrows on lines WX and YZ show
that the lines are parallel.
Holt CA Course 1
8-2 Geometric Relationships
Perpendicular lines intersect to form 90o
angles, or right angles.
Line RS is perpendicular to line TU.
RS __
| TU.
Holt CA Course 1
8-2 Geometric Relationships
Skew lines are lines that lie in different planes.
They are neither parallel nor intersecting.
Line AB and line ML are skew lines.
AB and ML are skew.
Holt CA Course 1
8-2 Geometric Relationships
Additional Example 1: Identifying Lines in Space
Identify two lines that have the given
relationship.
A. parallel lines
The lines are in the
same plane and do
not intersect.
AB || DC
Holt CA Course 1
A
D
B
C
E
8-2 Geometric Relationships
Additional Example 1: Identifying Lines in Space
Identify two lines that have the given
relationship.
B. perpendicular lines
The lines intersect
to form 90o angles.
CD __
| CE
Holt CA Course 1
A
D
B
C
E
8-2 Geometric Relationships
Caution!
Two lines may be perpendicular even though
they do not appear to be perpendicular. Use
the markings on the drawings and read the
problem carefully to determine which lines are
perpendicular.
Holt CA Course 1
8-2 Geometric Relationships
Additional Example 1: Identifying Lines in Space
Identify two lines that have the given
relationship.
C. skew lines
The lines lie in
different planes.
They are neither
parallel nor
intersecting.
AD and CE
Holt CA Course 1
A
D
B
C
E
8-2 Geometric Relationships
Check It Out! Example 1
Identify two lines that have the given
relationship.
A. perpendicular lines
The lines insect to
form 90o angles.
NP  PS
Holt CA Course 1
8-2 Geometric Relationships
Check It Out! Example 1
Identify two lines that have the given
relationship.
B. skew lines
The lines lie in
different planes.
They are neither
parallel nor
intersecting.
NP and QR
Holt CA Course 1
8-2 Geometric Relationships
Check It Out! Example 1
Identify two lines that have the given
relationship.
C. parallel lines
The lines are in the
same plane and do
not intersect.
NR and PS
Holt CA Course 1
8-2 Geometric Relationships
Holt CA Course 1
8-2 Geometric Relationships
Additional Example 2: Identifying Planes in Space
Identify two planes that appear to have the
given relationship.
K
A. perpendicular planes
The planes
intersect to form
right angles.
plane MPL  plane NPL
Holt CA Course 1
N
L
J
M
P
8-2 Geometric Relationships
Remember!
A plane may be named by any three points
that are not on the same line.
Holt CA Course 1
8-2 Geometric Relationships
Additional Example 2: Identifying Planes in Space
Identify two planes that appear to have the
given relationship.
K
B. parallel planes
The planes do not
intersect.
plane JKL || plane MNP.
Holt CA Course 1
N
L
J
M
P
8-2 Geometric Relationships
Additional Example 2: Identifying Planes in Space
Identify two planes that appear to have the
given relationship.
C. neither perpendicular nor parallel planes
K
The planes
intersect, but they
do not form right
L
J
angles.
plane JMN and plane MPL.
Holt CA Course 1
M
N
P
8-2 Geometric Relationships
Check It Out! Example 2
Identify two planes that appear to have the
given relationship.
D
A. perpendicular planes
The planes
intersect to form
right angles.
B
plane BAC  plane EAC
E
A
Holt CA Course 1
F
C
8-2 Geometric Relationships
Check It Out! Example 2
Identify two planes that appear to have the
given relationship.
D
B. parallel planes
B
The planes do not
intersect.
plane BAC || plane DEF
E
A
Holt CA Course 1
F
C
8-2 Geometric Relationships
Check It Out! Example 2
Identify two planes that appear to have the
given relationship.
C. neither perpendicular nor parallel planes
D
The planes
intersect, but they
B
do not form right
angles.
plane AEF and plane BDF
E
A
Holt CA Course 1
F
C
8-2 Geometric Relationships
Lesson Quiz: Part I
Identify two lines that have the given
relationship.
1. parallel lines
FK || EJ
2. perpendicular lines
FK  KJ
3. neither perpendicular nor parallel
FE and DH
Holt CA Course 1
8-2 Geometric Relationships
Lesson Quiz: Part II
Identify two planes that appear to have
the given relationship.
4. parallel planes
plane SPQ || plane WTU
5. perpendicular planes
plane PSW  plane WSR
6. neither perpendicular nor parallel
plane PQU and plane RQU
Holt CA Course 1
8-2 Geometric Relationships
Classwork & Homework
Lesson 8-2 Practice B
Lesson 8-2 Problem Solving
Holt CA Course 1
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