What is an Undefined Term in Geometry? 

The word “undefined” is commonly used in mathematics to describe terms that do not fit into pre-existing axiomatic systems. This includes terms such as point, line, and angle in the field of geometry and functions like cot th and csc th in set theory. 

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In the world of geometry, there are three major undefined terms: a point, a line, and a plane. These may be considered to be the building blocks of Euclidean geometry. 

A Point: 

The most fundamental of the geometrically related concepts is a point, which represents the position (or a point in space) with zero dimensions. It is a dot with a capital letter and can be drawn in many different ways, as shown in Figure 1. 

A Line: 

The other most important of the geometrically related concepts is a line, which extends in one dimension but has no thickness. This is a very interesting concept in geometry and is usually symbolized with a zigzag or a straight line containing two arrowheads. 

A Plane: 

The third of the geometrically related concepts is a plane, which has no thickness but extends indefinitely in all directions. This is a very interesting concept in both geometry and set theory, but is usually cryptic and hard to decipher. 

The name “plane” may be a bit overused, but it is still a very important concept in both the field of geometry and set theory. It can be modeled in many ways, but there is only one truly appropriate symbol and that is the trapezoid.