Chapter 3
Axioms for Plane Geometry
3.2 Distance and Ruler Postulate
The next axiom addresses what is to be assumed regarding the undefined term,
distance.
Axiom 3.2.1 (The Ruler Postulate).
For every
Chapter 3
Axioms for Plane Geometry
3.3 Plane Separation
In this section we will examine how and line divides a plane into two half-
planes, which will lead us to the definition of angle. We begin wit
Chapter 3
Axioms for Plane Geometry
3.7 The Parallel Postulates and Models
The geometry that can be done using only the six postulates stated in this chapter is
called neutral geometry.
Absolute geomet
Chapter 3
Axioms for Plane Geometry
3.5 The Crossbar Theorem and the Linear Pair Theorem
In this section we will state two fundamental theorems (without proof)the
Crossbar Theorem and the Linear Pair Th
Chapter 2
Axiomatic Systems and Incidence Geometry
2.5 Theorems, Proof, and Logic
At this point we examine the third part of an axiomatic systemthe
theorems and proofs. It should be clear that a major
Chapter 3
Axioms for Plane Geometry
3.6 The Side-Angle-Side Postulate
In this section we will examine the relationship between the length of
segments and angle measure and the best way to do so is thr
Chapter 3
Axioms for Plane Geometry
3.4 Angle Measure and the Protractor Postulate
In this section we discuss the last undefined termangle measure.
Axiom 3.4.1 (The Protractor Postulate).
For every
Chapter 2
Axiomatic Systems and Incidence Geometry
2.2 An Example: Incidence Geometry
Next we give a more mathematical and rigorous example of what an
axiomatic system is, the example of incidence geomet
Chapter 2
Axiomatic Systems and Incidence Geometry
2.3 The Parallel Postulates in Incidence Geometry
The purpose of this section is to gain a better understanding of Euclids Fifth
Postulate, referred to as
Chapter 1
Euclids Elements
1.0 Geometry Before Euclid
The word Geometry comes from the Greek words geo which means earth and
metron which means measurementthat is, the measurement of the earth.
[It] is a
Chapter 3
Axioms for Plane Geometry
Introduction
In this chapter you will be introduced to six axioms, which will lay the
foundation to all geometries studied throughout this course. Specifically, the
geo
Chapter 2
Axiomatic Systems and Incidence Geometry
2.6 Some Theorems from Incidence Geometry
We now have built up enough information to try and prove some theorems
from incidence geometry. Since the theo
Chapter 2
Axiomatic Systems and Incidence Geometry
2.4 Axiomatic Systems and the Real World
A nave view of geometry is that it is a branch of mathematics concerned with
questions of shape, size, and t
Chapter 2
Axiomatic Systems and Incidence Geometry
In this chapter we will examine the fundamental components of an axiomatic
systemits parts and the relationship between its parts. We will explore an
example o