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Angles and
Parallel Lines
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Transversal
Definition: A line that intersects two or more lines in a plane at
different points is called a transversal.
When a transversal t intersects line n and m, EIGHT angles are formed
m
t
Exterior angles: Outside the lines
Interior angles : Between the lines
n
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Vertical Angles & Linear Pair
Vertical Angles:
Two angles that are opposite angles.
Vertical angles are congruent.
 1   4,  2   3,  5   8,  6   7
Linear Pair:
Supplementary angles that form a straight line (sum = 180)
1 & 2 , 2 & 4 , 4 &3, 3 & 1,
5 & 6, 6 & 8, 8 & 7, 7 & 5
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Corresponding Angles
Corresponding Angles: Two angles, on the same side of the transversal, that
occupy corresponding positions, one interior and one exterior.
 2 and  6,  1 and  5,  3 and  7,  4 and  8
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Alternate Angles
Alternate Interior Angles: Two angles that lie between the lines on opposite
sides of the transversal (but not a linear pair).
 3 and  6,
 4 and 5
Alternate Exterior Angles: Two angles that lie outside the lines on opposite
sides of the transversal.
 2 and  7,
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3
5
7
 1 and  8
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4
6
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Consecutive Angles
Consecutive Interior Angles: Two angles that lie between the lines, both on the
same side of the transversal.
3 and 5 ,
4 and 6
Consecutive Exterior Angles: Two angles that lie outside the lines, both on the
same side of the transversal.
1 and 7 ,
2 and 8
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Example
List all pairs that fit the description
a. Corresponding
< 4 and < 2
< 3 and < 1
< 5 and < 7
b. Alternate Exterior
< 4 and < 8
< 1 and < 5
c. Alternate Interior
< 2 and < 6
< 3 and < 7
d. Consecutive Interior
< 3 and < 2
< 6 and < 7
< 6 and < 8
Example
Complete the statement with corresponding, alternate exterior,
alternate interior, or consecutive interior.
1. < 4 and < 8 are Alternate interior
2. < 2 and < 6 are Alternate exterior
3. < 1 and < 8 are Consecutive interior
4. < 7 and < 2 are Consecutive exterior
5. < 4 and < 6 are Corresponding
6. < 5 and < 7 are Vertical
Investigation
Let’s check out the
relationship of these angle pairs!
Angles and Parallel Lines
If two parallel lines are cut by a transversal, then the following
pairs of angles are CONGRUENT.
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Corresponding angles
Alternate interior angles
Alternate exterior angles
If two parallel lines are cut by a transversal, then the following
pairs of angles are SUPPLEMENTARY.
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•
Consecutive interior angles
Consecutive exterior angles
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Example
Given a ll b, find each measure given that m < 6 = 67°.
m6 
m7 
m8 
m9 
m10 
m11 
m12 
m13 
Example
State the postulate or theorem that justifies the statement.
3   7
3   6
2  7
m4  m6  180
Example: If line AB is parallel to line CD and s is parallel to t, find the measure of
all the angles when m< 1 = 100°. Justify your answers.
A
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4
C
5
8
m<2=80° m<3=100° m<4=80°
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B
D
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16 15
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s
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t
m<5=100° m<6=80° m<7=100° m<8=80°
m<9=100° m<10=80° m<11=100° m<12=80°
m<13=100° m<14=80° m<15=100° m<16=80°
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Example: If line AB is parallel to line CD and s is parallel to t, find:
1. the value of x, if m<3 = 4x + 6 and the m<11 = 126.
2. the value of x, if m<1 = 100 and m<8 = 2x + 10.
3. the value of y, if m<11 = 3y – 5 and m<16 = 2y + 20.
ANSWERS:
A
1
4
1. 30
C
8
2. 35
3. 33
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s
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9
12
3
6
13 14
16 15
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10
11
B
D
t
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