Components of Mathematical System Words and Statements 1. Undefined terms. 2. Definitions 3. Postulates 4. Theorems

Undefined Terms PLP: Point, Line and Plane 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. PLP: Point, Line and Plane

Point Has no dimension: no length, width, or thickness It only indicates place or position. Usually represented by a small dot A The above is called point A. Note the point is represented with a capital letter.

Line Has one dimension. An infinite set of points extending endlessly in two directions. Represented as a straight line with two arrowheads. l B A This is line l, (using the lower case script letter) or symbolically we call it NOTICE: The arrowheads are in both directions on the symbol

Plane Extends in two dimensions. A flat surface extending indefinitely in all directions Represented by a slanted 4 sided figure, but you must envision it extends without end, even though the representation has edges. A This is Plane m or plane ABC (be sure to only use three of the points when naming a plane) m C B

Line Plane

Circular Definitions Why Undefined terms? How do you define the first word without other words? Have you ever looked up a word that was explained in terms of another word that you did not know? Have you looked up the new word to find that it was defined in terms or the first word? This can be a real problem. In foreign languages this happens all the time. This also happens in geometry.

Geometric Example Definition #1 A point is the intersection of two lines. Definition #2 A line is a continuous series of points going in opposite directions.

This is a never ending cycle. What is wrong? 1 You need to know what a line is to define a point. 2 You need to know what a point is to define a line. This is a never ending cycle.