Geometry
Unit 3
Equations of Lines/Parallel & Perpendicular Lines
Lesson
Assignment
174(14, 15, 20-37, 44)
Parallel Lines & Transversals
181(11-19, 25, 27) *TYPO in student
edition book #27
Angles & Parallel Lines
Worksheet
Slopes of Lines
Quiz Review
Quiz
200(13, 16, 18, 19, 23, 25, 26, 29, 31, 32, 39,
40, 43-47)
Equations of Lines
208-209(2, 4, 8-15, 16, 18, 20, 33, 34)
Proving Lines Parallel
219(13, 14, 15, 18, 23, 32)
Perpendiculars & Distance
Review
Test
Parallel
Consecutive Interior
Slope
Slope Intercept Form
VOCABULARY
Skew
Interior Angles
Alternate Interior
Alternate Exterior
Perpendicular
Transversal
Point Slope Form
Exterior Angles
Corresponding
Distance
Geometry
Parallel Lines & Transversals
An Ames room creates the illusion that a person standing in the right
corner is much larger than a person standing in the left corner.
(See identical twins, right.)
From a viewing hole, the front and back walls appear parallel, when
in fact they are slanted. The ceiling and floor appear horizontal, but
are actually tilted.
The construction of the Ames room above makes use of intersecting, parallel,
and skew lines, as well as intersecting and parallel planes, to create an optical
illusion.
Parallel & Skew
Parallel lines are coplanar lines that do not intersect.
Example: JK || LM
J
K
L
M
Arrows are used to indicate that lines are parallel.
__________________________________________________________________________
Skew lines are lines that do not intersect and are not coplanar.
Example: Lines l and m are skew.
l
A
Parallel planes are planes that do not intersect.
Example: Planes A and B are parallel.
B
m
A line that intersects two or more coplanar lines at two different points is called a transversal.
Transversal Angle Pair Relationships
 3,  4,  5,  6
Four interior angles lie in the
region between lines q and r.
 1,  2,  7,  8
Four exterior angles lie in the
two regions that are not
between lines q and r.
 4 and  5,  3 and  6
Consecutive interior angles
are interior angles that lie on
the same side of the transversal.
 3 and  5,  4 and  6
Alternate interior angles are
nonadjacent interior angles that
lie on opposite sides of
transversal t.
 1 and  7,  2 and  8
Alternate exterior angles are
nonadjacent exterior angles that
lie on opposite sides of
transversal t.
Corresponding angles lie on
the same side of transversal t
and on the same side of lines q
and r.
 1 and  6,  2 and  5,
 3 and  8,  4 and  7
Geometry
Angles & Parallel Lines
Corresponding Angles Postulate
If two parallel lines are cut by a transversal, them each pair of corresponding angles is congruent.
Examples:
1 2
8 7
Example:
3 4
6 5
In the figure, m  8 = 105. Find the measure of each angle. Tell which postulate or
theorem you used.
t
m  1 = _______________________
m  2 = _______________________
1 2
4 3
n
m  3 = _______________________
m  4 = _______________________
m  5 = _______________________
m  6 = _______________________
m  7 = _______________________
Alternate Interior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of
alternate interior angles is congruent.
Examples:
Consecutive Interior Angles Theorem
If two parallel lines are cut by a transversal, then each pair of
consecutive interior angles is supplementary.
Examples:
Alternate Exterior Angles Theorem
If two lines are cut by a transversal, then each pair of alternate
exterior angles is congruent.
8 7
5 6
p
Perpendicular Transversal Theorem
In a plane, if a line is perpendicular to one of the two
parallel lines, then it is perpendicular to the other.
Example:
t
a
If line a ||b and line a  line t, then line b  line t.
b
Geometry
Slopes of Lines
Ski resorts assign ratings to their ski trails according to their
difficulty. A primary factor in determining this rating is a
trail’s steepness or slope gradient. A trail with a 6% or
6
100
vertical
rise
grade falls 6 feet vertically for every 100 feet traveled
horizontally.
The easiest trails have slopes ranging from 6% to 25%, while
more difficult trails have slopes of 40% or greater.
horizontal run
Slope of a Line
m=
y y2  y1
=
x x2  x1
(  means ________________ or ________________)
Example:
Find the slope of each line.
1A) ______________________
the line containing (6, -2) and (-3, -5)
1B) ______________________
the line containing (8, -3) and (-6, -2)
1C) ______________________
the line containing (4, 2) and (4, -3)
1D) ______________________
the line containing (-3, 3) and (4, 3)
Classifying Slopes
Positive Slope
Negative Slope
Zero Slope
Undefined slope
Slope can be interpreted as a rate of change, describing how a quantity y changes in relationship to
quantity x. The slope of a line can also be used to identify the coordinates of any point on the line.
Example:
DOWNLOADS – In 2006, 500 million songs were legally downloaded from the
Internet. In 2004, 200 million songs were legally downloaded.
A) Use the data given to graph the line that models the number of songs legally
downloaded y as a function of time x in years.
B) Find the slope of the line and interpret its meaning.
C) If this trend continues at the same rate, how many songs will be legally
downloaded in 2010?
 Parallel & Perpendicular Lines
You can use the slopes of two lines to determine whether the lines are parallel or perpendicular.
Lines with the same slope are _______________. Lines with slopes that are negative reciprocals
of each other are ________________.
Example:
Determine whether AB and CD are parallel, perpendicular or neither.
A) A(14, 13), B(-11, 0), C(-3, 7), D(-4, -5)
B) A(3, 6), B(-9, 2), C(5, 4), D(2, 3)
Geometry
Equations of a Line
Slope-intercept form_______________________________________________________
m=_______________
b=________________
Point slope form__________________________________________________________
m=_______________
(x1, y1)=___________________
Ex 1: Write an equation in slope intercept form if the slope is 3 and y-intercept is -2.
Graph the line.
Ex 2: Write an equation in point slope form if m=-3/4 that contains (-2,5). Graph the line.
Ex 3: Write an equation of a line that contains (0, 3) and (-2, -1) in slope intercept form.
Ex 4: Write an equation of a line that contains (-2, 6) and (5, 6) in slope intercept form.
**Key Concept**
X=a
is a vertical line
Y=b is a horizontal ine
Ex 5: Write an equation in slope intercept form for a line perpendicular to the line y=-3x+2 and goes
through (4, 0).
Geometry
Proving Lines Parallel
Postulate 3.4 If corresponding angles are congruent then the lines are parallel.
Ex
Theorems Summary:
Ex 1 Determine if the lines are parallel given the following information:
A <1=<6
B <2=<3
Ex 2 Find m<MRQ so that a // b. Show your work:
Geometry
Perpendiculars and Distance
Equidistant:___________________________________________________________________
___________________________________________________________________
Ex 1 Construct the segment that represents the distance indicated.
Ex 2 Line l contains points at (-5, 3) and (4, -6). Find the distance between line l and point (2, 4).
( Do ALL WORK on GRAPH PAPER ).
Ex 3 Find the distance between parallel lines l and m if their equations are y=2x+1 and y=2x-4
respectively.