Geometry
Name_________________________
WARM UP
Use the diagram to identify the types of angles.
1.  5 and  7
1
3 4
7 8
2
5 6
2.  3 and  6
3.  1 and  8
9 10
11 12
13 14
15 16
4. What is the slope of the line containing the points (2, 7) and (3, –10)?
5. What do you know about the slopes of…
- parallel lines?
- perpendicular lines?
Today, we will understand angle relationships of parallel lines cut by a
transversal
And, you will be able to prove two lines are parallel showing these
relationships.
Using Parallel Lines and Transversals & Proving Lines are Parallel
corresponding angles
alternate interior angles
2
2
6
6
4
5
alternate exterior angles
1
1
8
8
4
5
consecutive interior angles
3
5
5
3
Example 1
Find the value of x.
115
4
(x + 5)
Example 2
Use the diagram at the right.
 If m1 = 105°, find m4, m5, and m  8.
a.

1 2
3 4
b. If m  3 = 68° and m  8 = (2x + 4)°, what is the value of x?
Example 3
Find the value of x that makes m n.
(3x + 5)
m
65
n
Example 4
Find the value of x.
135
(x - 30)
Example 5
Find the value of y that makes a b.
(5y + 6)
a
121
b
5 6
7 8
Example 6
Can you prove that lines a and b are parallel? Explain why or why not.
a.
b.
a
b
a
Example 7
Find the value of x that makes m n.
m
n
a.
b.
b
n
m
(2x + 20)
(180 - x)
x
3x
MORE PRACTICE ON BACK
Practice – parallel lines and transversals
Find the value of each variable.
1.
y
2.
106
3.
80
y x
(x + 15)
x
4.
5.
6.
120
75
92
(5x - 10)
3x
(2x - 4)
Find the value of x that makes the two lines parallel.
7.
8.
100
110
80
(x - 15)
2x
10.
9.
(x + 1)
11.
(5x + 23)
12.
(x + 20)
4x (6x - 44)
(7x + 13)
x