PARALLEL LINES, TRANSVERSALS

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PARALLEL LINES, TRANSVERSALS AND SPECIAL ANGLES
Section 3-1, 3-2
Jim Smith JCHS
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A Line That Intersects 2 Or More Lines At
Different Points Is Called A Transversal
transversal
3
When This Happens, 8 Angles Are Formed
4
This Forms 2 Neighborhoods
5
Remember Vertical And Linear Angles
Vertical
3
7
5
1
4
6
8
2
6
Linear Pairs
3
7
5
1
4
6
8
2
7
These Angles Are Called Consecutive Or Same Side
Angles
8
Interior Angles (Between 2 lines)
Exterior Angles (outside the lines)
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Alternate Angles Are On Different Sides Of The
Transversal And From Different Neighborhoods
Alternate Exterior Angles 1 And 8 Angles 2 And
7 Alternate Interior Angles 3 And 6 Angles 4 And
5
5
1
3
7
4
6
8
2
10
Consecutive Int Angles 3 and 5 Angles 4 and 6
5
3
4
6
Consecutive Ext Angles 1 and 7 Angles 2 and 8
1
7
8
2
11
3
7
5
1
4
6
8
2
Corresponding Angles Are Located In The Same
Position In Each Neighborhood
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Name The Angles

1. 11 and 15
2. 12 and 16
3. 13 and 16
4. 12 and 18
5. 14 and 16
6. 14 and 18
7. 11 and 14
8. 15 and 17

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Check Your Answers

1. Corresponding
2. Corresponding
3. Alt Interior
4. Consecutive (SS) Exterior
5. Consecutive (SS) Interior
6. Corresponding
7. Vertical
8. Linear

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• Name the angles
• 1 and 3
• 7 and 12
• 11 and 14
• 6 and 10
• 13 and 5
• 9 and 6
• 1 and 13
• 5 and 4
• 7 and 11
• 6 and 11

4
3
2
1
8
7
6
5
12
11
10
9
16
15
14
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With This Diagram, We Can Work With Angles In
Different Neighborhoods As Long As They Are
Connected By A Transversal
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Check Your Answers

1. Corresponding
2. Alt. Int.
3. Alt. Int.
4. Cons. (SS) Int.
5. Corresponding
6. Alt. Int.
7. Consecutive Ext
8. Alt. Ext
9. Cons. (SS) Int.
10. None

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Parallel lines Lines that are coplanar and do not
intersect
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If 2 Parallel Lines Are Cut By A Transversal
Then
Corresponding Angles Are Congruent
Alternate Interior Angles Are Congruent
Same Side Interior Angles Are Supplementary
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Remember Even Without Parallel
Lines Vertical Angles Are Always Congruent
Linear Pairs Are Always Supplementary
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m 1 105

• Find
• 3
• 6
• 7
• 4
• 5

75 75 75 105 105
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119
63
1
2
a
117
119
61
3
4
119
63
63
6
5
b
8
7
119
21
2x6
4x25
5x-20
3x-10
6x-15
2x-10
4x25 6x-15 25 2x-15 40 2x 20
x
2x6 3x-10 6 x 10 16 x
5x-202x-10 180 7x-30 180
7x 210 x 30