Components of Mathematical System

1. Undefined terms.

2. Definitions

Words and Statements

3. Postulates

4. Theorems

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

Undefined Terms

Basics of Geometry

• Has no dimension: no length, width, or thickness

• It only indicates place or position.• Usually represented by a small dot

Point

A

The above is called point A. Note the point is represented with a capital letter.

Basics of Geometry

• Has one dimension.• An infinite set of points extending endlessly in two directions.

• Represented as a straight line with two arrowheads.

Line

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

l

B

A

Basics of Geometry

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

BC m This is Plane m or plane ABC (be

sure to only use three of the points when naming a plane)

Plane

Line

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.

Circular Definitions

Geometric ExampleDefinition #1A point is the intersection of two lines.

Definition #2A line is a continuous series of points going in opposite directions.

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.