Geometry

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Geometry

• Chapter 3 Using Parallel and Perpendicular Lines

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3.1 Parallel Lines and Transversals

• Identify the angle pairs formed by parallel lines
  and a transversal

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What you know

• Parallel Lines

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Topic 1 Parallel Lines and Skew Lines

• Parallel Lines that never touch and go in the
  same direction

• Skew Lines Lines that never touch but do NOT go
  in the same direction

j k
m n
AB is skew to SD
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Examples
List all the pairs of Parallel Lines
List all pairs of skew lines
AB CD
AB is skew to ED
CA DB
AB is skew to EC
CD is skew to EB
CD is skew to EA
CA is skew to EB
CA is skew to ED
BD is skew to EC
BD is skew to EA
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Topic 2 Transversals

• A transversal is a line that crosses any two
  other lines

j is a transversal for l and k
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Examples
What is the transversal for n and k?
What is the transversal for m and k?
m is the transversalit crosses both
n is the transversalit crosses both
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Topic 3 Corresponding Angles

• Corresponding Angles Same positiondifferent
  line

If n is the transversal
?5 is on the top left
?9 is on the top left
So ?5 and ?9 are corresponding angles
?4 and ?2 are corresponding angles
?10 and ?6 are corresponding angles
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Example
If k is the transversal find all the pairs of
corresponding angles
?9 corresponds with
?6
?11 corresponds with
?7
?12 corresponds with
?8
?10 corresponds with
?5
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Topic 4 Alternate Interior Exterior
If k is the transversal

• Alternate angles opposite side of the
  transversal
• Interior angles In between the two lines
• Exterior angles Outside the two lines

?4, ?3, ?6, ?5 are inside the other lines they
are INTERIOR
?1, ?2, ?8, ?7 are outside the other lines they
are EXTERIOR
?3, ?6 are on opposite sides of the
transversalthey are ALTERNATE INTERIOR
So are ?4 and ?5
?1, ?8 are on opposite sides of the
transversalthey are ALTERNATE EXTERIOR
So are ?2 and ?7
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Topic 5 Consecutive Interior
If k is the transversal

• Consecutive Interior Angles that are Interior
  and on the same side of the transversal

?3 and ?5 are Consecutive Interior
?4 and ?6 are Consecutive Interior
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Example

• For each pair of angles listed
• Find the transversal that forms them
• Determine whether they are
• Alternate Interior
• Consecutive Interior
• Alternate Exterior
• Corresponding

?9 and ?6
Transversal l
Both inside, and on the same side of
transversal Consecutive Interior
Transversal j
?1 and ?12
One inside, one out. Both on the left and top of
the transversal Corresponding
Transversal j
?10 and ?1
Both outside, on opposite sides of the
transversal Alternate Exterior
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Assignment

• HW Pg 128, 22-32 evens