PP Sections 1.2 and 2.1

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Geometry Sections 1.2 & 2.1
The Building Blocks of Geometry
In our study of geometry, in order
to avoid circular definitions, we will
leave 3 terms undefined.
point:
Usually described as a dot but
actually has no size. Named by a
capital letter.
Note: When you see a capital letter in a figure,
it represents a point even if the point is not
drawn.
line:
A set of points that continues on
without end in two opposite
directions. Named by a single lower
case letter ( line m or m )or any two
points on the line ( AB or BA ).
plane:
A set of points that extends
without end in 2 dimensions.
Named by a single capital letter
placed in a corner (plane M or M )
or by 3 points that do not all lie
in the same line ( plane BCA )
Points are collinear if they lie on
the same line.
In the description of a plane, we
talked about 3 points not on the
same line. Three points not on the
noncollinear
same line are called ___________.
1) Draw an example of four collinear points
2) Draw an example of four noncollinear points
Points are coplanar if they lie on
the same plane.
Points are noncoplanar if they do
NOT lie on the same plane.
1)Draw an example of four coplanar points.
2) Draw an example of four noncoplanar points.
Example: Determine if the given set of points are
collinear, coplanar, both or neither.
1) B, D
both
2) E, F, A
coplanar
3) B, C, D, E
neither
4) E, F, G, A
neither
Just as undefined terms are the
starting point for the vocabulary of
geometry, postulates are going to be
the starting point for the rules of
geometry. A postulate or axiom is
a statement that is accepted as true
without proof.
Postulate 5: Through any two
points there is exactly one line.
lines must be straight
Postulate 8: Through any three
noncollinear points there is exactly
one Plane.
Postulate 9: A plane contains at
least 3 noncollinear points.
Postulate 10: If two points lie in a
plane then the line containing
them is in the plane.
Postulate 11: If two planes
intersect, then their intersection is
a line.
A line segment or segment is part of a
line that begins at one point and ends
at a second. Segments are named by
their two endpoints ( AB or BA ).
A ray is a part of a line that begins
at one point and extends infinitely
in one direction. Rays are named
by their endpoint and another
point on the ray (________).
BA or BC

The intersection (symbol: ______)
of two (or more) geometric figures
is the set of points that are in both
figures at the same time.
Examples
A
1. Ray AC
2. Ray BD
B
C



3. Segment AB
D
ray CA
ray CA
segment BC
The union (symbol: ______)
 of two
(or more) geometric figures is the
set of points that are in one figure
or the other or both.
Examples
A
1. Line AB
B



2. Line segment AB
3. Ray BD
D
C
ray BC
line segment BC
ray CA
Example: Determine the following intersections
and unions based on the figure below.
DI
FH
DI
Example: Determine the following intersections
and unions based on the figure below.
F
GE


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