Undefined Terms and Intuitive Concepts
of Geometry
Undefined terms:
In geometry, definitions are formed using
known words or terms to describe a new word. There are three words
in geometry that are not formally defined. These three
undefined terms are point, line and plane.
POINT
(an undefined term)
In geometry, a point has no dimension
(actual size). Even though we represent a point with a dot, the
point has no length, width, or thickness. Our dot can be very
tiny or very large and it still represents a point. A point is usually
named with a capital letter. In the coordinate plane, a point is
named by an ordered pair, (x,y). 

LINE
(an undefined term)
In geometry, a line has no thickness but its length extends in
one dimension and goes on forever in both directions. Unless
otherwise stated a line is drawn as a straight line with two arrowheads indicating that the
line extends without end in both directions. A line is named by a
single lowercase letter,
,
or by any two points on the line,
. 

PLANE
(an undefined term)
In geometry, a plane has no thickness but extends indefinitely
in all directions. Planes are usually represented by a shape
that looks like a tabletop or a parallelogram. Even though the diagram of a
plane has edges, you must remember that the plane has no boundaries.
A plane is named by a single letter (plane m) or by three noncollinear
points (plane ABC). 

Intuitive Concepts:
There are a few basic concepts in geometry that need to
be understood, but are seldom used as reasons in a formal proof.
Collinear Points 
points that lie on the same line. 
Coplanar points 
points that lie in the same plane. 
Opposite rays 
2 rays that lie on the same line,
with a common endpoint and no other points in common. Opposite
rays form a straight line and/or a straight angle (180°:). 
Parallel lines 
two coplanar lines that do not
intersect 
Skew
lines 
two
noncoplanar lines that do not intersect. 
