Transcript Visual Representations of Geometry Building Blocks

Geometry 1-3
Segments, Rays, and Distance
Review: The Point
The point is an exact location
Like an infinitely small dot
Named with a capital letter
Q
Point Q
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
Review: The Plane
If we string and infinite number of lines
in both directions…
Named with three or more
A two-dimensional plane is formed.
points in the plane
The Ray
If we string an infinite number of points
straight out in only one direction…
A one-dimensional ray is formed
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.
Chop!
Going on forever
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)
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
A line segment is formed.
N
O
It is like a line that has been chopped at both ends.
Double
Chop!
ON
The Segment
Segment -- a piece of a line with a specific length
A
B
AB
“segment AB”
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
Notebook Terms
• Postulate or Axiom – a statement that is
accepted as true
• Theorem – a statement that can be proven
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.
Segment Addition
If B is between A and C then,
AB + BC = AC
A
B
53
Z
x + 12
I
2x – 7 P
C
Congruent
• Same size, same shape
• Congruent segments have equal lengths
Midpoints and Bisectors
The midpoint of a segment is in the exact middle
A bisector is anything that passes through the midpoint