Transcript Lecture-4_1 Parallel_skew _ perpendicular

Chapter 4.1
Skew, Parallel and
Perpendicular Lines
Objectives: We’ll learn…
• Define the characteristics of skew,
parallel and perpendicular lines.
Skew Lines
Skew lines lie in
different planes.
They are
•Not parallel
•Not intersecting
•Not perpendicular.
Skew lines
Skew lines are noncoplanar lines.
(Noncoplanar lines cannot intersect.)
SKEW LINES
•
Lines that lie in different planes.
They are neither parallel nor
intersecting.
SKEW LINES
• Lines that lie in different planes.
They are neither parallel nor
intersecting. G
B
F
A
H
E
D
C
CD and FA are SKEW LINES
FA and BD are SKEW LINES
Use the figure to find the following:
A
E
B
F
D
H
Two pairs of
Parallel Lines
AB CD
GC HD
C
G
Two pairs of
Parallel Planes
Two pairs of
Skew Lines
Plane AED Plane BCF AD, BF
Plane EFG Plane ABC EH, CG
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PARALLEL LINES
• Def: lines that do not intersect; must be
coplanar.
B
• Illustration:
A
l
C
m
• Notation:
D
l || m
AB || CD
p. 129
Two lines are parallel if they do not intersect.
A
B
C
D
A B CD
Read as line AB is parallel to line CD.
EX1: Are the lines parallel?
Examples of Parallel Lines
•
•
•
•
•
Hardwood Floor
Opposite sides of windows, desks, etc.
Parking slots in parking lot
Parallel Parking
Streets: Laramie & LeClaire
Examples of Parallel Lines
• Streets: Belmont & School
PERPENDICULAR LINES
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• Def: Lines that intersect to form a right
angle.
m
• Illustration:
n
• Notation: m  n
• Key Fact: 4 right angles are formed.
p. 79
PERPENDICULAR
•
Lines that intersect to form
right angles.
90° 90°
90°90°
When two lines intersect at right angles,
TRICK: 4 right angles are formed, but it shows 1 only. (The other 3 are invisible.)
They are called perpendicular lines.┴
Ex. of Perpendicular Lines
• Window panes
• Streets: Belmont and Cicero
Language of Geometry
Parallel lines & Transversal
Angles, Parallel Lines &
Transversal
Homework
p. 144,
1-9,
15-17