Angles

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SPECIAL RELATIONSHIPS BETWEEN

• Angles
• Parallel Lines
• Transversals

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Transversal

• A line that intersects two or more lines in
  a plane.
• When transversal t intersects lines m and n,
  eight angles are formed.
• These angles may be classified as
• corresponding angles
• alternate exterior angles
• alternate interior angles
• consecutive (same side) interior angles
• consecutive (same side) exterior angles

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Adjacent Angles
A pair of angles that lie in the same plane and
have a common vertex and a common side (lie next
to each other).

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

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Vertical Angles
A pair of opposite congruent angles formed by
intersecting lines.
? 1 ? ? 4, ? 2 ? ? 3, ? 5 ? ? 8, ? 6 ? ? 7
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Linear Pairs
Supplementary angles that form a line. The sum
of the angles equals 180?.
?1 ?2 , ?2 ?4 , ?4 ?3, ?3 ?1, ?5 ?6,
?6 ?8, ?8 ?7, ?7 ?5
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Angles and Parallel Lines

• If two parallel lines are cut by a transversal,
  then the following pairs of angles are congruent
  (same measure).
• 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 (sum 180).
• Consecutive (same side) interior angles
• Consecutive (same side) exterior angles

Continued..
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Corresponding Angles

• Two angles that occupy the same relative
  position, like top left, bottom left, top right,
  bottom right.

? 1 ? ? 5, ? 2 ? ? 6, ? 3 ? ? 7, ? 4 ? ? 8
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Consecutive (Same Side) Angles

• Same Side Interior Two angles that lie between
  parallel lines on the same side of the
  transversal.
• Same Side Exterior Two angles that lie outside
  parallel lines on the same side of the
  transversal.

m?3 m?5 180º, m?4 m?6 180º
m?1 m?7 180º, m?2 m?8 180º
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Alternate Angles

• Alternate Interior Angles Two angles that lie
  between parallel lines on opposite sides of the
  transversal (but not a linear pair).
• Alternate Exterior Angles Two angles that lie
  outside parallel lines on opposite sides of the
  transversal.

? 3 ? ? 6, ? 4 ? ? 5
? 2 ? ? 7, ? 1 ? ? 8
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Example If line AB is parallel to line CD and s
is parallel to t, find the measure of all the
angles when . Justify your
answers using appropriate vocabulary based on
special angle relationships.
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Example
If line AB is parallel to line CD and s is
parallel to t, find
ANSWERS
1. 30
2. 35
3. 33
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