# 8.2 Geometric Relationships (Parallel and Perpendicular Lines

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```					8.2 Geometric
Relationships
(Parallel
and Perpendicular
Lines)
Parallel and Perpendicular Lines

Perpendicular Lines meet at a right angle
l2

l1  l2

l1
Parallel and Perpendicular Lines

Parallel Lines never intersect
l3

                      l1  l2
l1

l3 is a
                            transversal
l2
Parallel and Perpendicular Lines
l3

l1



l2

The red arrows (or any arrows) on the lines
show that the lines are parallel.
Parallel and Perpendicular Lines

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.
Parallel and Perpendicular Lines
Identifying Lines in Space
Identify two lines that have the given
relationship.

A. parallel lines
A       B
The lines are in the        D
same plane and do                   C
not intersect.
E
AB || DC
Parallel and Perpendicular Lines
Identifying Lines in Space
Identify two lines that have the given
relationship.

B. perpendicular lines
A          B
The lines intersect         D
to form 90o angles.                    C

|
CD __ CE                              E
Parallel and Perpendicular Lines

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.
Parallel and Perpendicular Lines

Identifying Lines in Space
Identify two lines that have the given
relationship.

C. skew lines
A          B
The lines lie in           D
different planes.                     C
They are neither
parallel nor
intersecting.                         E

Parallel and Perpendicular Lines
Parallel and Perpendicular Lines

Identifying Planes in Space
Identify two planes that appear to have the
given relationship.

A. perpendicular planes            K

The planes                                N
intersect to form
right angles.              J       L

plane MPL  plane NPL          M         P
Parallel and Perpendicular Lines

Remember!
A plane may be named by any three points
that are not on the same line.
Parallel and Perpendicular Lines

Identifying Planes in Space
Identify two planes that appear to have the
given relationship.

B. parallel planes                 K

N
The planes do not
intersect.                         L
J
plane JKL || plane MNP.
M         P
Parallel and Perpendicular Lines

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                           N
do not form right
angles.                    J              L

plane JMN and plane MPL.       M              P

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