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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.
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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). |
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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,
 . |
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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 non-collinear
points (plane ABC). |
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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. |
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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). |
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Parallel lines |
two coplanar lines that do not
intersect |
| Skew
lines |
two
non-coplanar lines that do not intersect. |
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