Download Smart Board Notes 1-7 Postulates.notebook

Smart Board Notes 1­7 Postulates.notebook
September 07, 2012
Geometry 1.7
Postulates for Euclidean Geometry
Sep 12­8:55 AM
Chapter Vocabulary
Euclidean geometry:
Postulate:
Theorem:
Assumption
Have been proven true
Point – Line – Plane Postulate:
Unique Line Assumption:
Number Line Assumption:
Dimension Assumption:
Between any two points there is only ONE line connecting them.
On a number line,any place can be given zero, and any place to the right can be given one. 1. Given a line in a plane, there's at least one point in a plane not on the line.
2. Given a plane in space, there is at least one point in space not on the plane. Sep 10­7:21 AM
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Smart Board Notes 1­7 Postulates.notebook
September 07, 2012
Line Intersection Theorem: Two lines intersect at MOST one time
Parallel lines:
Two lines in the same plane are parallel if and only if they never intersect!
Sep 6­1:53 PM
Symbols!
Sep 7­10:13 AM
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Smart Board Notes 1­7 Postulates.notebook
September 07, 2012
1. Which two times of geometry that we’ve discussed so far are Euclidean?
Assume 2 – 7 questions are working in Euclidean geometry.
2. True or false: A point can be represented by an ordered pair of real numbers.
3. True or false: Lines have thickness.
4. True or false: Any line may be coordinatized using the real numbers.
5. True or false: Two different lines cannot intersect at two different points.
6. True or false: Lines are not dense.
7. True or false: Lines are parallel if they have no points in common or if they are on the same line.
Sep 6­1:53 PM
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Smart Board Notes 1­7 Postulates.notebook
September 07, 2012
Sep 6­1:54 PM
Sep 6­1:54 PM
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Smart Board Notes 1­7 Postulates.notebook
September 07, 2012
Sep 6­1:54 PM
Sep 6­1:55 PM
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Smart Board Notes 1­7 Postulates.notebook
September 07, 2012
Geometry 1.7 Postulates for Geometry
A starting point for proving a statement, also called an assumption
A Postulate is _____________________________________________________.
Through any two points, there is exactly one line.
Line Assumption:________________________________________. In Discrete, points have size This is only true for Synthetic Geometry. Why? ___________________________________.
so:
Every line could be made a number line Number Line Assumption ___________________________________________.
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How many points determine a line? __________________________________.
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How many points determine a plane? _________________________________.
There is a least 1­point in a plane not on a line in the plane. Draw this!
This is called the Dimension Assumption
Sep 10­7:12 AM
A Theorem is a statement which follows from postulate or definitions.
Line intersection theorem:
Lines intersect at exactly one point. Draw this!
line intersection theorem
This is called_________________________.
Parallel line definition:
Parallel lines are lines in the same plane that do not cross. Draw this!
Skew lines are lines that don’t cross and are not parallel.
Sep 10­7:17 AM
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