Honors Geometry Section 1.1
The Building Blocks of Geometry
Webster’s New World Dictionary, Third College Edition,
gives the following definitions.
turn: to rotate or revolve
rotate: to turn or cause to turn
revolve: to turn
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 )
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 ___________.
Points are collinear if they lie on
the same line.
Points are coplanar if they lie on
the same plane.
Noncoplanar?
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 1.1.4: The intersection of
two lines is a point.
Postulate 1.1.5: The intersection of
two planes is a line.
What important idea about planes is
indicated by this postulate?
planes continue on without end
Postulate 1.1.6: Through any two
points there is exactly one line.
What important idea about lines is
indicated by this postulate?
lines must be straight
Postulate 1.1.7: Through any three
noncollinear points there is exactly
one plane.
What if the three points were collinear?
infinitely many planes contain
collinear points
Postulate 1.1.8: If two points lie in
a plane then the line containing
them is in the plane.
What important idea about planes is indicated by this
postulate?
planes must be flat
While it certainly may seem as though these postulates
are not saying anything of any real importance, nothing
could be farther from the truth. These postulates are
in fact the basis of Euclidean geometry. For Euclid,
planes are a flat surface like the floor and lines are
straight like your pen or pencil. But what if we thought
of a plane as being the surface of a sphere (i.e. the
globe) and lines as being great circles on the sphere
(i.e. the equator or any lines of longitude). Such
thinking results in a whole
different type of geometry
called spherical geometry.
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
coplanar
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.

The union (symbol: ______) of two
(or more) geometric figures is the
set of points that are in one figure
or the other or both.
Example: Determine the following intersections
and unions based on the figure below.
DI
Example: Determine the following intersections
and unions based on the figure below.
DI
FH
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
Example: Determine the following intersections
and unions based on the figure below.
F
GE
Example: Determine the following intersections
and unions based on the figure below.
F
GE

Example: Assume the two given figures are not
the same figure and that the two figures have at
least one point in their intersection. Determine
all possible intersections of the two figures.
a. two lines
A point
Example: Assume the two given figures are not
the same figure and that the two figures have at
least one point in their intersection. Determine
all possible intersections of the two figures.
b. a plane and a line
A point
A line
Example: Assume the two given figures are not
the same figure and that the two figures have at
least one point in their intersection. Determine
all possible intersections of the two figures.
c. Two rays
A point
A line Segment
A ray