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Undefined Terms in Geometry
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An ‘undefined term’ is a term or word that doesn’t require further explanation or description. It already exists in its most basic form. These basic terms are used to define or explain more complicated terms or concepts.
Geometry recognizes four undefined terms. While some books only recognize three terms, all four will be included here. Even though they are ‘undefined’, I will attempt to describe them for you below.
Set – a group or collection with common characteristics
Example: A set of 10-year-old boys
A set of points on a line
A set of all even integers
Point – a dot on a page. A point has no dimensions (length, width, height), it is usually represent by a capital letter and a dot on a page. Think of it as an infinitely small place or position on a map.
Line – an unlimited number of points along the same path. The set of points may be straight or form a curve. Normally, the term ‘line’ means a straight line. The ‘line’ has no dimensions (length, width, height) and extends unlimited in both directions. (The part of a line defined by two points, called ‘endpoints’, is call a line segment or ‘segment’.) A ‘line’ is represented by a drawn line with arrowheads on each end to represent that it doesn’t have endpoints. A line can be named in two ways: (1) use the capital letters representing two points on the line and place a double-headed arrow above the two letters (2) use a lowercase letter beside the line to represent it.
Plane – a flat surface that extends indefinitely in all directions. It is usually represented by a parallelogram (four sided figure) with a capital letter in one corner. Remember the plane is not limited by the parallelogram, it extends infinitely. The plane can also be represented by using three points that lie on the plane surface but not on the same line (noncollinear).
See the article on ‘Defined Terms’ for more important information.
