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Pairs of Lines. Lesson 3-1. Parallel Lines. Parallel lines are coplanar lines that do not intersect. Arrows are used to indicate lines are parallel. The symbol used for parallel lines is ||. In the above figure, the arrows show that line AB is parallel to line CD. - PowerPoint PPT Presentation
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Lesson 3-1
Pairs of Lines
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Parallel Lines Parallel lines are coplanar lines that do not intersect. Arrows are used to indicate lines are parallel. The symbol used for parallel lines is ||.
DC
BA
In the above figure, the arrows show that line AB is parallel to line CD.With symbols we denote, .AB CD
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PERPENDICULAR LINES
Perpendicular lines are lines that intersect to form a right angle.
The symbol used for perpendicular lines is . 4 right angles are formed.
m
nIn this figure line m is perpendicular to line n.
With symbols we denote, m n
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OBLIQUE LINES
Oblique lines are lines that intersect, but do NOT form a right angle.
m n
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Skew Lines and Parallel Planes
Two lines are skew if they do not intersect and are not in the same plane (not coplanar).
Ex: All planes are either parallel or intersecting. Parallel planes are
two planes that do not intersect.
H
E
G
DC
BA
F
CG and EF���������������������������������������� ���
Ex: Plane ABC and Plane EFG
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Examples: 1. Name all segments that are parallel to2. Name all segments that intersect 3. Name all segments that are skew to4. Name all planes that are parallel to plane ABC.
Answers:1. Segments BC, FG, & EH.2. Segments DH, DC, AE & AB.3. Segments CG, BF, FE, & GH.4. Plane FGH.
ADAD
AD
H
E
G
DC
BA
F
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Slope of Parallel and Perpendicular lines
The slope of the non vertical line through the points and is
m =
The slope of a vertical line is not defined.The slope of a horizontal line is zero.
Two lines are parallel if and only if they have equal slopes.Two lines are perpendicular if and only if the product of
their slopes is -1 (reciprocals and opposite signs).
1 1( , )x y
2, 2( )x y2 1
2 1
y y
x x
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Examples:
a. (-4, 7) and (3, 7)
b. (3, -1) and (3, 2)
c. (1, -4) and (2, 5)
d. (-2, 5) and (1, -1)
7 7 00,
3 ( 4) 7horizontal line
Find the slope of the line through the given points.
2 ( 1) 3, .
3 3 0 v .
which is not defined
The line is a ertical line
5 ( 4) 99
2 1 1
1 5 62
1 ( 2) 3
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ExamplesAny line parallel to a line with slope has slope _____.
Any line perpendicular to a line with slope has slope ___.
Any line parallel to a line with slope 0 has slope _____.
Any line perpendicular to a line with undefined slope has slope.
Any line parallel to a line with slope 2 has slope _____.
2
7 4
3
2
7 3
40
Zero Slope
2
