Download Definitions and concepts

Definitions and concepts
MA418
Spring 2010
McAllister
What are ……..?

Undefined terms

Definitions

Postulates and axioms

Theorems

An axiomatic system
Undefined terms

Figures or ideas that can be described, but
cannot be given precise definitions
◦ Point – location in space. 0-dimension
Indicated by a dot, Label with Capital Letters
A
◦ Line – infinite set of points. 1 – dimension
Indicated by
 Label with 2 points or a lower case letter.
◦ Plane – sheet of points. 2 – dimensions
Definitions
Figures and objects that are described in
terms of undefined terms, previously
defined terms, and postulates.
 We DEFINE space to be the set of all
points.
 We DEFINE a geometric figure to be a
subset of space. (p. 39)

Postulates (axioms)
Statements we assume to be true
 State relationships among defined and
undefined terms.

◦ Every line contains at least two distinct points
◦ Two points are contained in one and only one
line
◦ If two points are in a plane, then the line
containing these points is also in the plane
(p.40)
Theorems
 Deductions
that can be made from
undefined terms, definitions, postulates,
and already proven theorems
◦ The sum of the measures of the angles in a
triangle is 180⁰. (p. 66)
◦ The sum of the measures of the vertex
angles in a polygon with n sides is
(n2)180⁰. (p.68)
Axiomatic system
 An
idea structure
 Begins with a small set of undefined
terms and builds on them to produce
definitions, postulates and theorems.
◦ Euclidean
◦ Non-Euclidean (pp. 555 – 565)
 Taxicab geometry (p. 560)