Lesson 2-3
Pairs of Lines
Lesson 2-3: Pairs of Lines
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 ||.
A
C
B
D
In the above figure, the arrows show that line AB is parallel to
line CD.
With symbols we denote, AB CD .
Lesson 2-3: Pairs of Lines
2
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
In this figure line m is perpendicular to line n.
n
With symbols we denote, m  n
Lesson 2-3: Pairs of Lines
3
OBLIQUE LINES


Oblique lines are lines that intersect, but do NOT form
a right angle.
m  n
Lesson 2-3: Pairs of Lines
4
Skew Lines and Parallel Planes


Two lines are skew if they do not intersect and are not in the
same plane (not coplanar).
Ex: CG and EF
All planes are either parallel or intersecting. Parallel planes are
two planes that do not intersect.
A
Ex: Plane ABC and Plane EFG
D
C
E
F
H
Lesson 2-3: Pairs of Lines
B
5
G
Examples:
1.
2.
3.
4.
Name all segments that are parallel to AD
Name all segments that intersect AD
Name all segments that are skew to AD
Name all planes that are parallel to plane ABC.
A
Answers:
1. Segments BC, FG, & EH.
2. Segments DH, DC, AE & AB.
3. Segments CG, BF, FE, & GH.
4. Plane FGH.
D
B
C
E
F
H
Lesson 2-3: Pairs of Lines
G
6
Slope of Parallel and Perpendicular lines

The slope of the non vertical line through the points ( x1 , y1 )
and ( x2, y2 ) is
y2  y1
m=
x2  x1
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).
Lesson 2-3: Pairs of Lines
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Examples: Find the slope of the line through the given points.
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
0
  0, horizontal line
3  (4) 7
2  (1) 3
 , which is not defined .
33
0
The line is a v ertical line.
5  ( 4) 9
 9
2 1
1
1  5
6

 2
1  ( 2)
3
Lesson 2-3: Pairs of Lines
8
Examples
2
Any line parallel to a line with slope 2 has slope _____.
7
7
3
Any line perpendicular to a line with slope  4 has slope ___.
3
4
0
Any line parallel to a line with slope 0 has slope _____.
Any line perpendicular to a line with undefined slope has slope.
Zero Slope
2
Any line parallel to a line with slope 2 has slope _____.
Lesson 2-3: Pairs of Lines
9