Postulates and Theorems Relating Points, Lines, and Planes

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Postulates and Theorems Relating Points, Lines,
and Planes

• Lesson 1.5
• Pre-AP Geometry

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Lesson Focus

• Postulates are statements accepted as true
  without proof. Postulates are them used to prove
  theorems.
• This lesson begins the study of using postulates
  to prove theorems.

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Postulates

• A point is defined by its location.
• A line contains at least two points.
• A plane contains at least three points not all
  in one line.
• Space contains at least four points not all in
  one plane.

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Postulates

• Through any two points there is exactly one
  line.
• Through any three points there is at least one
  plane and through any three non-collinear points
  there is exactly one plane.
• If two points are in a plane, then the line that
  contains the point is in that plane.
• If two planes intersect, then their intersection
  is a line.

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Theorem

• If two lines intersect, then they intersect in
  exactly one point.

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Theorem

• Through a line and a point not in the line there
  is exactly one plane.

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Theorem

• If two lines intersect, then exactly one plane
  contains the lines.

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Review Quiz True or False

• A given triangle can lie in more than one plane.
• Any two points are collinear.
• Two planes can intersect in only one point.
• Two lines can intersect in two points.

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Review Quiz True or False

• A given triangle can lie in more than one plane.
  False. Through a line and a point not in the
  line there is exactly one plane.
• Any two points are collinear. True. If two
  planes intersect, then their intersection is a
  line.
• Two planes can intersect in only one point.
  False. If two planes intersect, then they
  intersection is a line.
• Two lines can intersect in two points. False.
  If two lines intersect, then they intersect in
  exactly one point.

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• Problem Set 1.5
• Written Exercises
• p.25 1 13 (odd), 14 - 20