Chapter 3: Parallel and
Perpendicular Lines
Lesson 1: Parallel Lines and
Transversals
Definitions
Parallel lines ( || )- coplanar lines that do
not intersect (arrows on lines indicate
which sets are parallel to each other)
 Parallel planes- two or more planes that
do not intersect
 Skew lines- lines that do not intersect but
are not parallel (are not coplanar)
 Transversal- a line that intersects two or
more lines in a plane at different points

Pairs of angles formed by parallel lines
and a transversal (see graphic organizer for examples)
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Exterior angles: outside the two parallel lines
Interior angles: between the two parallel lines
Consecutive Interior angles: between the two
parallel lines, on the same side of the transversal
Consecutive Exterior angles: outside the two
parallel lines, on the same side of the transversal
Alternate Exterior angles: outside the two
parallel lines, on different sides of the transversal
Alternate Interior angles: between the two
parallel lines, on different sides of the transversal
Corresponding angles: one outside the parallel
lines, one inside the parallel lines and both on the
same side of the transversal
A. Name all segments parallel to BC.
B. Name a segment skew to EH.
C. Name a plane parallel to plane ABG.
Classify the relationship between each set of angles as
alternate interior, alternate exterior, corresponding, or
consecutive interior angles
A. 2 and 6
B. 1 and 7
C. 3 and 8
D. 3 and 5
A. Identify the sets of lines to
which line a is a transversal.
B. Identify the sets of lines to
which line b is a transversal.
C. Identify the sets of lines to
which line c is a transversal.
Chapter 3: Parallel and
Perpendicular Lines
Lesson 2: Angles and Parallel
Lines
If two parallel lines are cut by a
transversal, then… (see graphic organizer)
the alternate interior angles are congruent
 the consecutive interior angles are
supplementary
 the alternate exterior angles are
congruent
 the corresponding angles are congruent
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In a plane, if a line is perpendicular to one
of the two parallel lines, then it is also
perpendicular to the other line.
A. In the figure, m11 = 51.
Find m15. Tell which
postulates (or theorems) you
used.
B. In the figure, m11 = 51.
Find m16. Tell which
postulates (or theorems) you
used.
A. In the figure, a || b and
m20 = 142. Find m22.
B. In the figure, a || b and
m20 = 142. Find m23.
A. ALGEBRA If m5 = 2x – 10,
and m7 = x + 15, find x.
B. ALGEBRA If m4 = 4(y – 25),
and m8 = 4y, find y.
A.
ALGEBRA If m1 = 9x +
6, m2 = 2(5x – 3), and
m3 = 5y + 14, find x.
B. ALGEBRA If m1 = 9x + 6,
m2 = 2(5x – 3), and
m3 = 5y + 14, find y.
Chapter 3: Parallel and
Perpendicular Lines
Lesson 5: Proving Lines Parallel
If…
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(see graphic organizer)
Corresponding angles are congruent,
Alternate exterior angles are congruent,
Consecutive interior angles are supplementary,
Alternate interior angles are congruent,
Two lines are both perpendicular to the
transversal,
Then the lines are parallel.
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If given a line and a point not on the line, there is
exactly one line through that point that is parallel
to the given line
If so, state the postulate or theorem that
justifies your answer.
A. Given 1  3, is it
possible to prove that any of
the lines shown are parallel?
B. Given m1 = 103 and
m4 = 100, is it possible to
prove that any of the lines
shown are parallel?.
Find ZYN so that
||
. Show your work.
A. Given 9  13, which segments are parallel?
B. Given 2  5, which segments are parallel?
___
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C. Find x so that AB || HI if m1 = 4x + 6 and
m14 = 7x – 27.
Chapter 3: Parallel and
Perpendicular Lines
Lesson 3: Slopes of Lines
Slope
The ratio of the vertical rise over the
horizontal run
 Can be used to describe a rate of change

Two non-vertical lines have the same
slope if and only if they are parallel
 Two non-vertical lines are perpendicular if
and only if the product of their slopes is -1
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Foldable

Step 1: fold the paper into 3 columns/sections

Step 2: fold the top edge down about ½ inch to form a
place for titles. Unfold the paper and turn it vertically.
Step 3: title the top row “Slope”, the middle row “Slopeintercept form” and the bottom row “Point-slope form”

Slope
y2  y1
m
x2  x1
Rise = 0
Run = 0
zero slope (horizontal line)
undefined (vertical line)
Parallel = same slope
Perpendicular = one slope is the reciprocal and opposite sign
of the other
Ex: find the slope of a line containing (4, 6) and (-2, 8)
Find the slope of the line.
Find the slope of the line.
Find the slope of the line.
Find the slope of the line.
Determine whether FG and HJ are parallel,
perpendicular, or neither for F(1, –3), G(–2, –1),
H(5, 0), and J(6, 3).
(DO NOT GRAPH TO FIGURE THIS OUT!!)
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Determine whether AB and CD are parallel,
perpendicular, or neither for A(–2, –1),
B(4, 5), C(6, 1), and D(9, –2)
A. Graph the line that contains Q(5, 1) and is
parallel to MN with M(–2, 4) and N(2, 1).
B. Graph the line that contains (-1, -3) and is
perpendicular to MN for M(–3, 4) and N(5, –8)?
Chapter 3: Parallel and
Perpendicular Lines
Lesson 4: Equations of Lines
Slope-intercept form:
y = mx + b
Slope and
y-intercept
Two ordered-pairs
(one is y-intercept)
Two ordered-pairs
(neither is y-intercept)
m = -4
y-intercept = 7
(4, 1) (0, -2)
(3, 3) (2, 0)
* This should be your middle row on the foldable
Point-slope form: y  y1  m( x  x1 )
Slope and one ordered-pair
m = 1
(7, 2)
Two ordered-pairs
(8, -2)
3
* This should be your bottom row on the foldable
(-3, -1)
Write an equation in slope-intercept
form of the line with slope of 6 and yintercept of –3.
Write the equation in slope-intercept form and then
Write an equation in point-slope form of the line
whose slope is
graph the line.
that contains (–10, 8). Then
Write an equation in slope-intercept
form for a line containing (4, 9) and
(–2, 0).
Write an equation in point-slope form
for a line containing (–3, –7) and
(–1, 3).
On the back:
Chapter 3: Parallel and
Perpendicular Lines
Lesson 6: Distance Between
Parallel Lines
Perpendicular Lines and Distance
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The shortest distance between a line and a point
not on the line is the length of the perpendicular
line connecting them
Equidistant: the same distance- parallel lines are
equidistant because they never get any closer or
farther apart
The distance between two parallel lines is the
distance between one line and any point on the
other line
In a plane, if two lines are equidistant from a
third line, then the two lines are parallel to each
other
Steps to find the distance between
parallel lines:
1.
2.
3.
4.
5.
Change the first equation so that the slope is
now perpendicular to the given slope. (do not
change anything else)
Set the new equation equal to the second given
equation
Solve for x.
Plug in for x in the new equation (the one with
the perpendicular slope) and solve for y.
Find the distance between the ordered pair
created with x and y and the y-intercept from
the changed equation (the one with
perpendicular slope).

Find the distance between each pair of
lines
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
y = 2x + 1
y = 2x - 4
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Find the distance
between the two
parallel lines
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y=
y=
1
4
1

4

x+2
9
x4