Chapter 3 Notes
Section 3-1, Parallel Lines and Transversals
Parallel Lines:
Symbols for Parallel Lines:
Parallel Planes:
Skew Lines:
Example 1: Use the picture to answer the following questions.
-A plane parallel to Plane OPT
-All segments parallel to NU
-All segments skew to MP
Example 2: Use the figure to answer the following questions.
-All segments parallel to QX
-All planes that intersect plane MHEN
-A segment skew to AG
Transversal:
_________________
Interior:
Exterior:
Example 3: Label the interior and exterior of each set of lines.
Special Angle Relationships
Alternate Interior Angles:
Identify the transversal first. Then the interior
and exterior.
Examples:
Same Side (Consecutive) Interior Angles:
Examples:
Alternate Exterior Angles:
Same Side (Consecutive) Exterior Angles:
Examples:
Examples:
Corresponding Angles:
Examples:
Example 4: Use the figure to identify the transversal that connects each pair of angles.
 9 and 13
1
9 10
n
12 11
2
4 3
5 6
8 7
13 14
16 15

5 and 14

4 and 6
l
Example 5: Use the figure to classify the relationship between each set of angles as alternate interior, alternate exterior,
corresponding, or consecutive interior angles.
 1 and 5
• 6 and 14
• 2 and 8
1
 3 and 11

6 and 16
•
•
12 and 3
11 and 14
ASSIGNMENT: pg. 174, 13-36 and 38-43
Due on Monday, October 12
•
•
4 and 6
10 and 16
2
4 3
5 6
8 7
9 10
n
12 11
13 14
16 15
l
Section 3-2, Parallel Lines and Angles
Review
Alternate Interior Angles:
Same Side Interior Angles:
Examples:
Examples:
Alternate Exterior Angles:
Same Side Exterior Angles:
Examples:
Examples:
Corresponding Angles:
Vertical Angles:
Linear Pairs:
Examples:
Examples:
Examples:
ANGLE PAIRS
When two parallel lines are cut by a transversal line, then…………
Alternate Interior Angles are _________________.
Examples:
Alternate Exterior Angles are _________________.
Examples:
Corresponding Angles are ___________________.
Examples:
Same Side Interior/Exterior Angles are ___________________________.
Examples:
Example 1:
Given: m1  64 Find the measures of the remaining numbered angles.
Example 2:
Find the measures of the numbered angles.
Example 3:
Given: m9  80 and m5  68
1 2
4 3
9 10
12 11
5 6
8 7
p
13 14
16 15
w
q
v
Example 4: Find the values of the variables.
 4z  6
o
xo
106o
2y
o
ASSIGNMENT: 3-2 Worksheet
Due on Tuesday, October 13
Find the measures of the remaining angles.
Section 3-5, Proving Lines Parallel
Remember, in section 3-2, we were saying that if two parallel lines are cut by a transversal, then there were a few
different angle relationships. Now, we’re doing the converse (flip).
Converse Corresponding Angles Theorem:
Given: 1  5
Which two lines are parallel?
These two lines could be proven parallel if 2  6, 4  8, and 3  7.
Converse Alternate Exterior Angles Theorem:
Given:
2  8
Which two lines are parallel?
These two lines can be proven parallel if 1  7.
Converse Alternate Interior Angles Theorem:
Given: D  E
r
Which two lines are parallel?
These two lines can be proven parallel if C  F .
s
Converse Same Side Interior Angles Theorem:
Given: m4  m6  180
Which two lines can be proven parallel?
If m3  m5  180, then the lines can be proven parallel as well.
Perpendicular Transversal Converse:
Line k and line l are both perpendicular to line t, so they are
parallel.
Example 1:
answer.
Use the picture to determine which, if any, lines are parallel. State the postulate that justifies your
•
3  7
•
6  13  180
•
12  10
•
9  10  180
•
3  9
•
12  14
•
4  10
Example 2:
Find x so that l is parallel to m. Identify the postulate or theorem that you used.
Example 3:
ASSIGNMENT:
Worksheet 3-5
Due on Thursday, Oct. 22
Section 3-3, Slopes of Lines
Slope:
Ways to find Slope:
Graph
Formula
Classifying Slope:
Example 1: Find the slope of each line.
Example 2: Find the slope of each line.
 J(0,0) K(-2,8)
● T(1,-2) U(6,-2)
●
P(-3,-5)
Q(-3,-1)
Slopes of Parallel Lines:
Slopes of Perpendicular Lines:
Example 3:
 M(0,3)

M(-1,3)
Example 4:
Determine whether MN and RS are parallel, perpendicular, or neither.
N(2,4) R(2,1) S(8,4)
N(0,5)
R(2,1)
S(6,-1)
Graph the line that satisfies the condition.
Passes through H(8,5), and perpendicular to AG with A(-5,6) and G(-1,-2)
Example 5:
Graph the line the satisfies the condition.
Slope = 4, passes through (6,2)
ASSIGNMENT: pg 191; 12-25, 28-39
Due on Monday, October 26
Section 3-4, Equations of Lines
NonVertical Line Equations
Slope Intercept Form
Point-Slope Form
Horizontal and Vertical Line Equations
Horizontal Lines
Vertical Lines
Example 1: Write an equation in slope-intercept form of a line having the given slope and y-intercept.
 m = 2, b = -3
1
,b=5
4

m=

m = 0, b = -2
Example 2:
Write an equation in point-slope form given the slope and a point.

3
m =  , (-2,5)
4

m = 4, (-3,-6)

m = 2, (5,2)
Example 3: Write an equation in point-slope form given two points. Use the first point in the set for the equation.
 (2,0) (0,10)
● (-3,-2) (-3,4)

(-12,-6)

(-1,-4)
(8,9)
●
(1,5)
(-7,5)
(3,-4)
●
(2,-1)
(2,6)

Remember, slopes of Parallel Lines are the SAME!!!
Slopes of Perpendicular Lines are the NEGATIVE RECIPROCALS or their product is -1.
Example 4:
Write an equation in point-slope form of a line that meets the following conditions.
 Perpendicular to y = -3x+2 and goes through (4,0)
3
x  3 and goes through (-3,6)
4

Parallel to y  

Parallel to y = 6, and goes through (1,5)

Parallel to x = -1, and goes through (2,-5)

Perpendicular to y = 1, and goes through (-4,-2)

Perpendicular to x = 5, and goes through (1,7)
ASSIGNMENT: pg 200; 13-30, 32, 34, 37-40, 46-49
Due on Tuesday, October 27