Geometry 1-3

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Geometry 1-3

• Segments, Rays, and Distance

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Review The Point
The point is an exact location
Like an infinitely small dot
Named with a capital letter
Point Q
Q
3
Review The Line
If we string an infinite number of points
straight out in both directions
A one-dimensional line is formed
Named with a lower case letter or two points on
the line
C
U
Going on forever
Going on forever
UC or CU
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Review The Plane
If we string and infinite number of lines in
both directions
Named with three or more points in the plane
A two-dimensional plane is formed.
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The Ray
If we string an infinite number of points
straight out in only one direction
A one-dimensional ray is formed
Chop!
Named with the endpoint and another point on the
ray
GZ
G
Z
It is like a line that has been chopped at one
end.
Going on forever
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The Ray
Ray a piece of a line that has one endpoint and
continues infinitely in only one direction
Opposite rays two rays with a common endpoint
that extend in opposite directions (making a line)
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The Segment
If we draw an infinite number of points between
2 endpoints, it gives us a piece of a line of
finite length
NO or ON
Double Chop!
A line segment is formed.
O
N
It is like a line that has been chopped at both
ends.
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The Segment
Segment -- a piece of a line with a specific
length
A
B
segment AB
AB
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Length

• length of a line segment length of a segment is
  defined as the distance between the endpoints of
  the segment
• --the length of AB (previous) would be denoted
  as AB

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Notebook Terms

• Postulate or Axiom a statement that is accepted
  as true
• Theorem a statement that can be proven

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Ruler Postulate

• Ruler Postulate any line can be made into a
  number line such that the distance between any
  two points is the absolute value of the
  difference of their coordinates.

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Segment Addition
If B is between A and C then, AB BC AC
A
C
B
53
Z
x 12
P
2x 7
I
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Congruent

• Same size, same shape
• Congruent segments have equal lengths

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Midpoints and Bisectors
The midpoint of a segment is in the exact middle
A bisector is anything that passes through the
midpoint