Angles and Parallel Lines

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Unit 1

• 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 of the following types are formed
• Exterior angles
• Interior angles
• Consecutive interior angles
• Consecutive exterior angles
• Alternate exterior angles
• Alternate interior angles
• Corresponding angles

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Corresponding Angles

• Corresponding Angles Two angles in the same
  position.
• These angles are congruent.

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2
3
4
5
6
7
8
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Alternate Interior Angles

• Alternate Interior Angles Two angles that are on
  opposite sides of the transversal and inside the
  parallel lines. These angles are congruent.
  Circle 4 and 5 as an example of this
  type.

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2
3
4
5
6
7
8
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Alternate Exterior Angles

• Alternate Exterior Angles Two angles that are on
  opposite sides of the transversal and outside the
  parallel lines. The angles are congruent.

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2
3
4
5
6
7
8
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Consecutive Interior Angles

• Consecutive Interior Angles Two angles on the
  same side of the transversal and inside the
  parallel lines. These angles are supplementary
  (180).

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2
3
4
5
6
7
8
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Consecutive Exterior Angles

• Consecutive Exterior Angles Two angles on the
  same side of the transversal and outside the
  parallel lines. These angles are supplementary (
  180).

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2
3
4
5
6
7
8
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Vertical Angles

• Vertical Angles

Two angles that are across from each other. These
angles are congruent.
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2
3
4
5
6
7
8
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Linear Pair

• Linear Pair

Supplementary angles that form a line (sum 180?)
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2
3
4
5
6
7
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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.
• 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.
• Consecutive interior angles
• Consecutive exterior angles
• Linear Pair

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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 mlt 1 100. Justify your answers.
mlt280 mlt3100 mlt480
mlt5100 mlt680 mlt7100 mlt880
mlt9100 mlt1080 mlt11100 mlt1280
mlt13100 mlt1480 mlt15100 mlt1680
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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 mlt3 4x 6 and the mlt11
126.
2. the value of x, if mlt1 100 and mlt8 2x
10.
3. the value of y, if mlt11 3y 5 and mlt16
2y 20.
ANSWERS
1. 30
2. 35
3. 33