Math 445 Geometry for teachers
Final guide and rules
Date: June 10, 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 10-13, 16, extra) (a
printed copy will be provided)
3. A two-sided page of notes handwritten or typed
up by you
Material:
Chapters 6-13, 16, student presentations, and homework. You should understand
the statements and proofs of all theorems in chapter 7, 9 - 13, and 16 (up to, but not
including, the “Constructible Points” section), 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 7.1, 7.8, 7.9, 7.15, 7.19, 7.25,
ii) Ch. 9 9.2,
9.9, 9.15,
iii) Ch. 10 10.1,
10.4, 10.8, 10.11, 10.19, 10.26, 10.28, 10.30 (Midsegment),
iv) Ch. 11. 11.11,
11.12,
v) Ch. 12. 12.2, 12.3,
12.9, 12.11 (Menelaus’, one direction),
vi) Ch. 13 13.1 (Pythagorean),
13.8, 13.9,
vii) Ch. 16 16.1, 16.5,
16.6, 16.17, 16.18, 16.28, 16.29
viii) Extra: Pick’s
formula (the case of a right triangle with sides parallel to the grid); Euler’s
formula for planar graphs.
2. Everything that was assigned as
homework:
i)
Ch.7 7.6, 7.7, 7.10, 7.13, 7.23,
ii) Ch. 9 9.4,
9.13, 9.19, 9.20,
iii) Ch. 10 10.7,
10.13, 10.14, 10.15,
iv) Ch. 11 11.10,
11.13,
v) Ch. 12 12.10
(same as Generalized Thales Theorem (Hw. 6, Pr.5)),
12.12 (Ceva), 12.15, 12.17,
vi) Ch. 13 13.2
(Converse to the Pythagorean),
vii) Extra: 14.25 (Hw. 8, pr. 3), 14.34 (Hw.9, pr. 3), Formula for the area of
a triangle: Hw. 8, pr. 5, Hw.
9, pr. 4
3. Additionally,
i)
Ch.7 7.18, 7.20, 7.21, 7.22,
ii) Ch. 9 9.3,
9.10, 9.11,
iii) Ch. 10 10.5,
10.6, 10.10, 10.12, 10.17, 10.18, 10.21,
iv) Ch. 12 12.19,
v) Ch. 13 13.3,
13.4, 13.5, 13.12, 13.13 (Law of Cosines), 13.14 (Law of Sines),
13.15 (Sum formulas), 13.16 (Double angle formulas).
vi) Theorems on concurrence of
(1) Medians
(2) Angle bisectors
(3) Altitudes
(4) Perpendicular bisectors
vii) Ch. 16 16.4,
16.27
4. Review ALL homework; know how to do
ALL homework problems correctly.
Review sessions:
1. June 6, 11:30-12:30 pm, Padelford C-36, by Graham
2. June 5th, in class.