1. Lesson 3-1: Pairs of Lines

2. Lesson 3-1: Pairs of Lines
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.
With symbols we denote,
Lesson 3-1: Pairs of Lines

3. Lesson 3-1: Pairs of Lines
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 n
In this figure line m is perpendicular to line n.
With symbols we denote, m  n
Lesson 3-1: Pairs of Lines

4. Lesson 3-1: Pairs of Lines
OBLIQUE LINES
Oblique lines are lines that intersect, but do NOT form a right angle.
m  n 
Lesson 3-1: Pairs of Lines

5. 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.
Ex: Plane ABC and Plane EFG
Lesson 3-1: Pairs of Lines

6. Lesson 3-1: Pairs of Lines
Examples:
Name all segments that are parallel to
Name all segments that intersect
Name all segments that are skew to
Name all planes that are parallel to plane ABC.
Answers:
Segments BC, FG, & EH.
Segments DH, DC, AE & AB.
Segments CG, BF, FE, & GH.
Plane FGH.
Lesson 3-1: Pairs of Lines

7. 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).
Lesson 3-1: Pairs of Lines

8. Lesson 3-1: Pairs of Lines
Examples:
Find the slope of the line through the given points.
(-4, 7) and (3, 7)
(3, -1) and (3, 2)
(1, -4) and (2, 5)
(-2, 5) and (1, -1)
Lesson 3-1: Pairs of Lines

9. Lesson 3-1: Pairs of Lines
Examples
Any 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 _____.
Zero Slope 2
Lesson 3-1: Pairs of Lines