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Holt CA Course 1 8-2 Geometric Relationships Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson Presentation Preview Preview
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Holt CA Course 1
8-2 Geometric Relationships
Warm UpWarm Up
California StandardsCalifornia Standards
Lesson PresentationLesson Presentation
PreviewPreview
Holt CA Course 1
8-2 Geometric Relationships
Warm UpUse the diagram to name each figure.
P, Q, R1. three points
plane PQR
P
Q
R
PQ2. a line
3. a plane
4. three rays
5. two segments
PQ, QP, QR
QP,QR
Holt CA Course 1
8-2 Geometric Relationships
MG3.6 Identify elements of three-dimensional geometric objects (e.g., diagonals of rectangles solids) and describe how two or more objects are related in space (e.g., skew lines, the possible ways three planes might intersect).
California Standards
Holt CA Course 1
8-2 Geometric Relationships
Vocabulary
parallel linesperpendicular linesskew linesparallel planesperpendicular 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
The red arrows on lines WX and YZ show that the lines are parallel.
Reading Math
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
Identify two lines that have the given relationship.
A. parallel lines
Additional Example 1: Identifying Lines in Space
The lines are in the same plane and do not intersect.
DC
BA
EAB || DC
Holt CA Course 1
8-2 Geometric Relationships
Identify two lines that have the given relationship.
B. perpendicular lines
Additional Example 1: Identifying Lines in Space
The lines intersect to form 90o angles.
DC
BA
ECD | CE __
Holt CA Course 1
8-2 Geometric Relationships
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.
Caution!
Holt CA Course 1
8-2 Geometric Relationships
Identify two lines that have the given relationship.
C. skew lines
Additional Example 1: Identifying Lines in Space
The lines lie in different planes. They are neither parallel nor intersecting.
DC
BA
E
AD and CE
Holt CA Course 1
8-2 Geometric Relationships
Check It Out! Example 1
NP PS
Identify two lines that have the given relationship.
A. perpendicular lines
The lines insect to form 90o angles.
Holt CA Course 1
8-2 Geometric Relationships
Check It Out! Example 1
NP and QR
Identify two lines that have the given relationship.
B. skew lines
The lines lie in different planes. They are neither parallel nor intersecting.
Holt CA Course 1
8-2 Geometric Relationships
Check It Out! Example 1
NR and PS
Identify two lines that have the given relationship.
C. parallel lines
The lines are in the same plane and do not intersect.
Holt CA Course 1
8-2 Geometric Relationships
Holt CA Course 1
8-2 Geometric Relationships
Identify two planes that appear to have the given relationship.
A. perpendicular planes
Additional Example 2: Identifying Planes in Space
The planes intersect to form right angles.
M
J
K
N
Pplane MPL plane NPL
L
Holt CA Course 1
8-2 Geometric Relationships
A plane may be named by any three points that are not on the same line.
Remember!
Holt CA Course 1
8-2 Geometric Relationships
Identify two planes that appear to have the given relationship.
B. parallel planes
Additional Example 2: Identifying Planes in Space
The planes do not intersect.
M
J
K
N
P
L
plane JKL || plane MNP.
Holt CA Course 1
8-2 Geometric Relationships
Identify two planes that appear to have the given relationship.
C. neither perpendicular nor parallel planes
Additional Example 2: Identifying Planes in Space
The planes intersect, but they do not form right angles.
M
J
K
N
P
L
plane JMN and plane MPL.
Holt CA Course 1
8-2 Geometric Relationships
Identify two planes that appear to have the given relationship.
A. perpendicular planes
Check It Out! Example 2
The planes intersect to form right angles.
plane BAC plane EAC
B
D
F
CA
E
Holt CA Course 1
8-2 Geometric Relationships
Identify two planes that appear to have the given relationship.
B. parallel planes
Check It Out! Example 2
The planes do not intersect.
plane BAC || plane DEF
B
D
F
CA
E
Holt CA Course 1
8-2 Geometric Relationships
Identify two planes that appear to have the given relationship.
C. neither perpendicular nor parallel planes
Check It Out! Example 2
The planes intersect, but they do not form right angles.
plane AEF and plane BDF
B
D
F
CA
E
Holt CA Course 1
8-2 Geometric RelationshipsLesson Quiz: Part I
Identify two lines that have the given relationship.
1. parallel lines
2. perpendicular lines
3. neither perpendicular nor parallel
FK || EJ
FK KJ
FE and DH
Holt CA Course 1
8-2 Geometric RelationshipsLesson Quiz: Part II
Identify two planes that appear to have the given relationship.
4. parallel planes
5. perpendicular planes
6. neither perpendicular nor parallel
plane SPQ || plane WTU
plane PSW plane WSR
plane PQU and plane RQU
