Intro to geometry notes i.notebook December 02, 2011 Undefined terms The terms point, line, and plane are accepted as intuitive ideas and are not defined. Opposite ray have a common endpoint and form a straight line. and are opposite rays. l
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Intro to geometry notes i.notebook December 02, 2011
Undefined termsThe terms point, line, and plane are accepted as intuitive ideas and are not defined.
Opposite ray have a common endpoint and form a straight line.
and are opposite rays.
l
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Intro to geometry notes i.notebook December 02, 2011
Postulate relating to lines.
Postulate:A line contains at least two points.Through any two points there exists one and only one line.
Theorems about Lines that we will not prove.
If two lines intersect, then they intersect in exactly one point.
Ruler Postulate: There is a unique measure that represents the distance between points A and B we call that measure AB or BA.
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Intro to geometry notes i.notebook December 02, 2011
Planes: A plane is a flat surface with no depth or boundary.
Coplanar points are points all in one plane.
non coplanar points.
Postulates:A plane contains at least three points not all in one line.
Through any three points there is at least one plane, and through any three noncollinear points there is exactly one plane.If two points are in a plane, then the line that contains the points is inthat plane.
If two planes intersect, then their intersection is a line.
A line can exist on an infinite number of planes.
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Intro to geometry notes i.notebook December 02, 2011
If two lines intersect, then they lie exactly on one plane.
Theorem about planes we won't prove:
Through a line and a point not in the line there is exactly one plane.
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Intro to geometry notes i.notebook December 02, 2011
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Intro to geometry notes i.notebook December 02, 2011
Betweeness
Is AC > AB?
AC = CB?
AC CB?
AC + CB = AC?
Segment Addition Postulate:
If C is between A and B, then AC + CB = AB
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Intro to geometry notes i.notebook December 02, 2011
Definition of Midpoint.
The midpoint of a segment is the point that divides the segments into two equal segments.
If M is the midpoint of segment AB, then AM = MB or
Definition of a bisector.
If a line, ray, line segment, or plane that intersects the segment at its midpoint, then it is the bisector of the segment.
Two objects that have the same size and shape are called congruent.
Congruent segments are segments that have equal lengths.
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Attachments
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