Parallel and Perpendicular Lines

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Parallel and Perpendicular Lines

• Lesson 13.3
• Pre-AP Geometry

2
Lesson Focus

• The purpose of this lesson is to state and apply
  two theorems that can be used to determine if two
  lines are parallel or perpendicular by comparing
  their slope.

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Parallel lines

• Two lines in the xy-plane may be classified as
  parallel or perpendicular based on their slope.
• Parallel and perpendicular lines have very
  special geometric arrangements most pairs of
  lines are neither parallel nor perpendicular.
• Parallel lines have the same slope.

4
Parallel Lines
For example, the lines given by the equations, y1
-3x 1, y2 -3x - 4, are parallel to one
another. These two lines have different
y-intercepts and will therefore never intersect
one another since they are changing at the same
rate (both lines fall 3 units for each unit
increase in x).
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Perpendicular Lines
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Theorem 13-3

• Two non-vertical lines are parallel if and only
  if their slopes are equal.

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Theorem 13-4

• Two non-vertical lines are perpendicular if and
  only if the product of their slopes is -1.
• or
• Two non-vertical lines are perpendiculars if and
  only if their slopes are negative reciprocals of
  each other.

8
Written Exercises

• Problem Set 13.3, p.537 2 - 10 (even)
  Handout 13-3