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Lesson 3-2
Objective- To find missing angles formed by
parallel lines and a transversal.
Parallel Lines Crossed by a Transversal
A
C
1 2
3 4
5 6
7 8
Corresponding Angles
1  5
 2  6
3  7
4  8
 
AB  CD
D
x  60
X
g
d e
f
130
c
a
b
3  6
4  5
ma  50
mb  130
mc  50
md 130
130
Z
Alternate Interior
Line X  Line Y
me  50
mf  130
mg  50
Alternate Exterior
1  8
 2  7
If parallel lines are cut by a
Corresponding
transversal, then the
Angles Postulate
corresponding angles are congruent.
x  60
2x  x  60
x  x
Y
B
Find y.
120
2x y
Find the missing angles.
If parallel lines are cut by a
Alternate Interior
- transversal, then the alternate
Angles Theorem
interior angles are congruent.
y  120  180
120  120
y  60
If parallel
ll l lines
li
are cutt by
b a
Alternate Exterior
- transversal, then the alternate
Angles Theorem
exterior angles are congruent.
2x  120
If parallel lines are cut by a
Same Side Interior
Angles Theorem transversal, then the same side
interior angles are supplementary.
Same Side Interior Angles Proof
1 2
Given a  b, prove 2 and 3 are suppl.
a
Statement
Reasons
Given
1) a  b
3
b
2) 1 & 2 are linear pair.
Def. of linear pair
3) 1 & 2 are suppl.
Linear Pair Theorem
4) m1  m2  180
Def of Suppl. Angles
5) 1  3
Corres. s  Post.
6) m1  m3
Def. of  s
7) m3  m2  180
Substitution (6 into 4)
8) 2 & 3 are suppl.
Def. of  s
Find each angle measure.
3x  20
x  40
3x  20  x  40  180
4x  20  180
 20  20
4x  200
x  50
3x  20 
3(50)  20  170
x  40 
50  40  10
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
1
Lesson 3-2
State the theorem or postulate that relates each
pair of angles, then find their measures.
State the theorem or postulate that relates each
pair of angles, then find their measures.
1) m4  3x  18
m8  x  54
2) m3  5x  20
m6  x  50
1 2
3 4
5 6
7 8
Corres. s Post.
3x  18  x  54
x
x
2x  18  54
 18  18
2x  36
x  18
1 2
3 4
5 6
7 8
Alt. Ext. s Thm.
m4  3x  18 
3(18)  18  72
m8  x  54 
18  54  72
5x  20  x  50
x
x
4x  20  50
 20  20
4x  30
x  7.5
m3  5x  20 
5(7.5)  20  57.5
m6  x  50 
7.5  50  57.5
State the theorem or postulate that relates each
pair of angles, then find their measures.
3) m4  3x  40
m7  5x  60
1 2
3 4
5 6
7 8
SS. Int. s Thm.
3x  40  5x  60  180
8x  20  180
 20  20
8x  160
x  20
m4  3x  40 
3(20)  40  20
m7  5x  60 
5(20)  60  160
Geometry Slide Show: Teaching Made Easy As Pi, by James Wenk © 2014
2