4.5 Introduction to Parallel Lines

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4.5 Introduction to Parallel Lines

• Advanced Geometry

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PARALLEL LINES

• Definition lines that do not intersect.
• Illustration
• Notation l m AB CD

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Examples of Parallel Lines

• Hardwood Floor
• Opposite sides of windows, desks, etc.
• Parking slots in parking lot
• Parallel Parking
• Streets Laramie LeClaire

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Examples of Parallel Lines

• Streets Belmont School

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PERPENDICULAR LINES

• Def Lines that intersect to form a right angle.
• Illustration
• Notation m ? n
• Key Fact 4 right angles are formed.

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Example Perpendicular Lines

• Window panes
• Streets Belmont and Cicero

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Transversal Lines
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• Def a line that intersects two lines at
  different points
• Illustration

t
p. 131
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Vertical Angles

• Two angles that share the same vertex and whose
  sides are formed by opposite rays.

t

• 1 ? ? 4
• 2 ? ? 3
• 5 ? ? 8
• 6 ? ? 7

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2
3
4
5
6
7
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Vertical Angles

• Find the measures of the missing angles

t
125 ?
125 ?
?
55 ?
?
55 ?
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Supplementary Anglesa.k.a Linear Pair

• Two angles that together form a line (sum180?)

t

• 5?6180
• 6?8180
• 8?7180
• 7?5180

• 1?2180
• 2?4180
• 4?3180
• 3?1180

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2
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4
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5
7
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Supplementary Angles/a.k.a. Linear Pair

• Find the measures of the missing angles

t
?
72 ?
108 ?
180 - 72
?
108 ?
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Corresponding Angles

• Two angles that occupy corresponding positions.

t

• 1 ? ? 5
• 2 ? ? 6
• 3 ? ? 7
• 4 ? ? 8

Top Left
Top Right
Bottom Left
Bottom Right
Top Left
Top Right
Bottom Left
Bottom Right
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Corresponding Angles

• Find the measures of the missing angles

t
35 ?
?
145 ?
Top Left !
Top Right !
?
35 ?
145 ?
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Alternate Interior Angles

• Two angles that lie between parallel lines on
  opposite sides of the transversal

Are you noticing the CONGRUENCE symbols?
t

• 3 ? ? 6
• 4 ? ? 5

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2
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4
5
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Alternate Interior Angles

• Find the measures of the missing angles

t
?
82 ?
98 ?
?
98 ?
82 ?
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Alternate Exterior Angles

• Pairs of angles that lie outside parallel lines
  
• on opposite sides of the transversal

t

• 2 ? ? 7
• 1 ? ? 8

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2
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4
5
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7
8
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Alternate Exterior Angles

• Find the measures of the missing angles

t
?
60
120 ?
?
60 ?
120 ?
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Consecutive Interior Angles

• Two pairs of angles between parallel lines
  on the same sides of the transversal

t
Be ALERT! These angle pairs are SUPPLEMENTAL,
NOT congruent!

• 3 ?5 180
• 4 ?6 180

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Same - Side Interior Angles
(Consecutive Interior Angles contd)

• These angles are also known as
  Same-Side Interior Angles
• and these angles are supplementary!

t

• 3 ?5 180
• 4 ?6 180

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2
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4
5
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7
8
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Consecutive Interior Anglesa.k.a. Same-Side
Interior Angles

• Find the measure of the missing angle

t
180 - 135
135 ?
?
45 ?
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Summary
If two lines are parallel and are intersected by
a transversal line resulting in eight angles,
then the following conclusions can be drawn
CONGRUENT Angle Pairs Include Vertical
Angles (4) Corresponding Angles (4)
Alternate Interior Angles (2) Alternate
Exterior Angles (2)
Other Types of Angle Pairs Include
Supplementary Pairs (4), a.k.a., Linear Pair
(4) Consecutive Interior Angles (2), a.k.a.,
Same-Side Interior Angles (2) All of these
form STRAIGHT ANGLES and have a sum of 180!
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? AS ?