Math 445 Geometry for teachers
Final guide and rules

Date: June 9, 8:30am, in class.
Closed book, closed notes, all electronic devices off and away, individual work only!
Allowed:

1.      List of axioms and theorems of Neutral geometry (Chapters 3-9) (a printed copy will be provided)

2.      List of axioms and theorems of Euclidean geometry (Chapter 10-14, 16, extra) (a printed copy will be provided)

3.       A two-sided page of notes handwritten or typed up by you

Material: Chapters 6-14, 16, student presentations, and homework. You should understand the statements and proofs of all theorems in chapter 7, 9 - 13, and the ones in chapters 14 and 16 which were covered in class. You are also responsible for the material of chapters 6 and 8 to the extent that was covered in class, and the material covered in presentations. The following theorems may appear explicitly on the final:

1.      Everything that was proven in class:

i)        Ch.7 7.19, 7.23, 7.25,

ii)      Ch.9 9.2, 9.10, 9.11, 9.15,

iii)    Ch.10 10.1, 10.4, 10.8, 10.11, 10.12, 10.19, 10.20, 10.23,

iv)    Ch.11 11.7, 11.11, 11.12,

v)      Ch.12 12.2, 12.3, 12.9, 12.12 (Ceva’s), 12.13,

vi)    Ch.13 13.1 (Pythagorean), 13.8, 

vii)  Ch.14 14.7, 14.16, 14.21, 14.28, 14.28, 14.35, 14.36,

viii)Ch.16 16.5, 16.6, 16.17, 16.18, 16.21, 16.28, 16.29,

ix)     Extra: Pick’s formula (the case of a right triangle with sides parallel to the grid); Euler’s formula for planar graphs, Concurrence results for Cevians (spelled out below), Compass & Straightedge construction results (from ch. 16, spelled out above).

2.      Everything that was assigned as homework:

i)        Ch.7 7.6, 7.7, 7.9, 7.13, 7.15 

ii)      Ch.9 9.4, 9.13, 9.19, 9.20,

iii)    Ch.10 10.7, 10.10, 10.13, 10.14, 10.15, 10.25

iv)    Ch.11 11.10, 11.11, 11.12, 11.13,

v)      Ch.12 12.5, 12.6, 12.8, Converse to the angle Bisector Proportion Theorem (ex.12D), 12.17,

vi)    Ch.13 13.2 (Converse to the Pythagorean), 13.14 (Law of Sines) (Hw. 8, pr 3) 

vii)   Ch.14 14.5, 14.17, 14.25 (Hw. 7, pr. 3),

3.       Extra: Formula for the area of a triangle: Hw. 7, pr. 4,

4.      Additionally,

i)        Ch.7 7.20, 7.21, 7.22,

ii)      Ch.9 9.9,

iii)    Ch.10 10.5, 10.6, 10.16, 10.17, 10.18, 10.28,

iv)    Ch.11 11.8, 11.9,

v)      Ch.12 12.15,

vi)    Theorems on concurrence of

(1)   Medians (12.13)

(2)   Angle bisectors (14.35)

(3)   Altitudes

(4)   Perpendicular bisectors

vii)  Ch. 16 16.1, 16.4, 16.27

5.      Review ALL homework; know how to do ALL homework problems correctly.

Review sessions:

1.      June 7th, 3-5pm, Padelford C-36, by Andrew

2.      June 6th, in class.