Undefined Terms
Point, Line and Plane

Topic Index | Geometry Index | Regents Exam Prep Center

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 non-collinear 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 non-coplanar lines that do not intersect.