# Parallel & Perpendicular Lines ```Parallel &amp; Perpendicular Lines
Chapter 3
Parallel Lines &amp; Transversals
Section 3.1
Vocabulary
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Parallel lines
Parallel planes
Skew lines
Transversal
Consecutive interior angles
Alternate interior angles
Alternate exterior angles
Corresponding angles
Example 1
Example 2
Identify the sets of lines to which each line is a transversal.
Angle Relationships
Example 3
Identify each pair of angles as alternate interior, alternate
exterior, corresponding, or consecutive interior angles.
Angles &amp; Parallel Lines
Section 3.2
Postulates &amp; Theorems
3.1 – Corresponding Angles Postulate - If 2 parallel lines are
cut by a transversal, then each pair of corresponding
angles is congruent.
Example 1
Example 1
Theorems
3.1 – Alternate Interior Angles – If two parallel lines are cut
by a transversal then each pair of alternate interior angles
is congruent.
3.2 – Consecutive Interior Angles – If two parallel lines are
cut by a transversal, then each pair of consecutive interior
angles is supplementary.
3.3 – Alternate Exterior Angles – If two parallel lines are cut
by a transversal, then each pair of alternate exterior
angles is congruent.
3.4 – Perpendicular Transversal Theroem – In a plane, if a
line is perpendicular to one of two parallel lines, then it is
perpendicular to the other.
Example 3
Example 3
Example 2 – Using an auxiliary line
Example 2 – Using an auxiliary line
Slopes of Lines
Section 3.3
Example 1
Example 1
Example 1
Example 1
Example 1
Find the slope of the line containing (-6, -2) and (3, -5).
Example 1
Find the slope of the line containing (8, -3) and (-6, -2).
Example 2
Between 2000 and 2003, annual sales of exercise equipment
increased by an average rate of \$314.3 million per year. In
2003, the total sales were \$4553 million. If sales of fitness
equipment increase at the same rate, what will the total
sales be in 2010?
Example 2
the Internet. In 2003, 20 million songs were legally
Postulates
3.2 Parallel Lines - Two nonvertical lines have the same
slope if and only if they are parallel.
3.3 Perpendicular Lines – Two nonvertical lines have are
perpendicular if and only if the product of their slopes is
-1. *Remember opposite reciprocals*
Example 3
Determine whether line AB and line CD are parallel,
perpendicular or neither.
A(-2, -5), B(4, 7), C(0, 2), D(8, -2)
Example 3
Determine whether line AB and line CD are parallel,
perpendicular or neither.
A(-8, -7), B(4, -4), C(-2, -5), D(1, 7)
Example 3
Determine whether line AB and line CD are parallel,
perpendicular or neither.
A(14, 13), B(-11, 0), C(-3, 7), D(-4, -5)
Example 3
Determine whether line AB and line CD are parallel,
perpendicular or neither.
A(3, 6), B(-9, 2), C(-12, -6), D(15, 3)
Example 4
Graph the line that
contains P(-2, 1) and is
perpendicular to
line JK with J(-5, -4)
and K(0, -2).
Example 4
Graph the line that
contains P(0, 1) and is
perpendicular to
line QR with Q(-6, -2)
and R(0, -6).
Equations of Lines
Section 3.4
Example 1
Write an equation in slope-intercept form of the line with
slope of -4 and y-intercept of 1.
Example 2
Write an equation in point-slope form of the line with a
slope of -1/2 that contains (3, -7).
Example 3
Write an equation in slope-intercept form for line l.
Example 3
Write an equation in slope-intercept form for the line that
contains (-2, 4) and (8, 10).
Example 4
Write an equation in slope-intercept form for a line
containing (2, 0) that is perpendicular to the line with
equation y = -x + 5.
Example 4
Write an equation in slope-intercept form for a line
containing (-3, 6) that is parallel to the line with equation
y = -3/4x + 3.
Example 5
Gracia’s current wireless phone plan charges \$39.95 per
month for unlimited calls and \$0.05 per text message.
Write an equation to represent the total monthly cost C
for t text messages.
Proving Lines Parallel
Lesson 3.5
Postulates
3.4 - If two lines are cut by a transversal so that
corresponding angles are congruent, then the lines are
parallel.
3.5 – Parallel Postulate – If given a line and a point not on
the line, then there exists exactly one line through the
point that is parallel to the given line.
Theorems
3.5 – If two lines are cut by a transversal so that a pair of
alternate exterior angles is congruent, then the two lines
are parallel.
3.6 – If two lines are cut by a transversal so that a pair of
consecutive interior angles is supplementary, then the
lines are parallel.
3.7 – If two lines are cut by a transversal so that a pair of
alternate interior angles is congruent, then the lines are
parallel.
3.8 – If two lines are perpendicular to the same line, then
they are parallel.
Example 1
Example 1
Example 2
Example 2
Example 3 – PROVING Lines Parallel
Given: r ∥ s; ∡5≅∡6
Prove: l ∥ m
Example 4
Determine whether g ∥ f.
Example 4
Line e contains points at (-5, 3) and (0, 4). Line m contains
points at (2, -2/3) and (12, 1). Determine whether the
lines are parallel.
Perpendiculars &amp; Distance
Section 3.6
Distance between a point &amp; a line
Example 1
Draw the segment that represents the distance from P to
line AB.
Theorem
3.9 – If two lines are equidistant from a third line, then the
two lines are parallel to each other.
Example 3
Fine the distance between the parallel lines l and n with
equations y = -1/3x-3 and y = -1/3x + 1/3 respectively.
Example 3
Fine the distance between the parallel lines a and b with
equations x + 3y = 6 and x + 3y = -14 respectively.
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