|
Undefined terms are those that we define by their usage. The best way to decribe them is by thinking of their "dimensions"
in the way we would say a picture is an 8 X 10. Well the 8 and the 10 are the two dimensions.
The four undefined terms are:
Point- no dimensions; a point has no "size" it only designates location...
Line- one dimesion; a line has length (infinite) but no width or "thickness"
Plane- two dimensions; the 8 X 10 picture is an example of a plane
Space- three dimensions; sometimes we say length, width and height.
Albert Einstein said "It is obvious that we live in a four dimensional space-time continuum."
I guess it's obvious if your Einstein.
The following is taken from www.regentsprep.org it gives us three of the four but it does a pretty good job.
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. 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. A line is depicted to be a straight line with two arrowheads indicating that the line extends without
end in two directions. A line is named by a single lowercase letter,  , or by 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 wall. 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 non-collinear points (plane ABC). |
|
Any two points can determine a unique line containing them.
| 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 (180º). |
| Parallel lines |
two coplanar lines that do not intersect |
|
