Math 444
Geometry for Teachers
Homework Expectations
Winter 2010
Due Date: Each written assignment has a due date; the assignment should be turned in at the beginning
of class on that day. Homework turned in after the ﬁrst ten minutes of class will get a

Math 444
Geometry for Teachers
Winter 2010
Some Challenge Problems
1. In the following diagram, AB = BC = CD and AD = BD. Find the measure of angle D.
D
C
A
B
←
→
←
→
2. In this diagram, AB is parallel to CD and the side lengths are as shown. Find the are

Math 444
Geometry for Teachers
Winter 2010
SYLLABUS
Professor:
John M. (Jack) Lee
Padelford C-546, 206-543-1735
lee@math.washington.edu
Oﬃce hours: to be announced.
TA:
Julie Eaton
Padelford C-404
jreaton@math.washington.edu
Discussion sessions: to be ann

Chapter 4
Proofs in Incidence Geometry
In this chapter, we will begin to discuss the process of constructing rigorous mathematical proofs. First, we discuss the general structure of proofs and describe some
“templates” for proofs of different types. Havin

Chapter 3
The Language of Mathematics
In the previous chapter, we introduced incidence geometry, and discussed three of its
four elements as an axiomatic system: undeﬁned terms, axioms, and deﬁnitions. We
have not yet introduced the fourth and most import

Chapter 2
Incidence Geometry
Motivated by the advances described in the previous chapter, mathematicians since
the early twentieth century have always proved theorems using what is now called
the axiomatic method. The purpose of this chapter is to describ

Chapter 1
Reading Euclid
The story of axiomatic geometry begins with Euclid, the most famous mathematician in history. We know very little about Euclid’s life, save that he was a Greek who
lived and worked in Alexandria, Egypt around 300 B . C . E . His m

Appendix D
Conventions for Writing Proofs
Writing mathematical proofs is, in many ways, unlike any other kind of writing.
Over the years, the mathematical community has agreed upon a number of moreor-less standard conventions for proof writing. This appen

Appendix C
Properties of the Real Numbers
Because our axioms for plane geometry are predicated on an understanding of the
real number system, it is important to establish clearly what properties of the real
numbers we are taking for granted. In this appen

Appendix B
Birkhoff’s Axioms for Plane Geometry
These axioms are taken from the 1932 article A set of postulates for plane geometry, based on scale and protractor, by George D. Birkhoff [GDB32]. In Birkhoff’s
system, the undeﬁned terms are point, line, di

Appendix A
Hilbert’s Axioms for Plane Geometry
These axioms are taken from The Foundations of Geometry by David Hilbert (1899),
as translated by E. J. Townsend in 1902 [DH02]. Although Hilbert’s treatment includes axioms for three-dimensional spatial geom