8D, 9B,9C

Additional problem: Given a polygon, show that there exists a line that does not intersect it. This might be tricky - be creative!

9D, 10A, 10D, 10E, 10F

Additional problem: Prove that any convex polygon with all of its angles acute is a triangle.

Quiz 1 covering chapters 8, 9, 10.

11A, 11B, 11C, 11D, 11G.

Turn in re-dos (or first attempts) for the additional problem originally due July 29. Turn in your original homework with grader comments so I can compare.

12A, 12C, 12H, 12K.

Additional problem: Prove that the ratio of the length of any diagonal to the length of any edge in a regular pentagon is the golden ratio.

13C,13H,13I, 13K

Additional problem: Give two more complete proofs of the Pythagorean theorem that we have not done in class/in the text. These could be 13A and/or 13B, or any other proofs you can find in other resources. If you make use of a figure make sure you describe how the figure can be constructed, and justify any claims you make about it.

Quiz 2 covering chapters 11, 12, 13.

14A, 14B, 14E, 14I, 14K, 14L.

12I, 14O, 14P, 14R, 14S. That's not a typo: 12I is needed for the Euler line theorem.

Bring a straightedge and compass with you if you have them, we may do a few constructions in class.

Quiz 3 covering chapters 14, 16.

16K, 16P, 16Q, 16S, 16T.

For each of the construction problems above (except 16S - see below), describe the construction and prove that it works. For writing style, you should follow the example of the solutions in the text. You can use the previously described constructions without explicitly describing each step. For example, you can say "Draw the perpendicular bisector of AB" if that construction problem has already been solved in the text.

In addition, perform the construction with compass and straightedge on a blank, unlined page and turn this in with the problem. If a point or line is named (A, B, C, etc.) in your solution you should label it as such in the construction.

In 16S, you are asked to construct a pentagon. The description of this solution is already given in the text, so if you follow this construction you do not need to write anything for this problem. Alternately, you may find a different construction of a pentagon - in this case, write a brief description of your construction.

Check out this page for some fun compass and straightedge construction challenges.

Quiz 4 covering Chaper 17, and Chapter 18 through Theorem 18.9.

18B, 18C, 18D, 18E, 18F.

Send me an email suggesting something you'd like me to review before the final exam.

Review for final. I will select three or four out of the following problems to put on the final. In addition, there will be one or two proof problems that are not on this list, and other problems where you do not need to prove anything.

In neutral geometry:

Theorem 9.12 (SASAS Congruence)
Theorem 17.2. (Proving that the Equidistance Postulate implies the Euclidean Parallel Postulate)

In Euclidean geometry:

Theorem 10.1 (Converse to the Alternate Interior Angles Theorem)
Theorem 10.14 (30-60-90 Theorem)
Theorem 10.17 (AAA Construction Theorem)
Lemma 11.9 (Area of a Right Triangle)
Theorem 12.5 (SSS Similarity Theorem)
Theorem 13.1 (The Pythagorean Theorem)
Theorem 14.16 (Thales' Theorem.)
Construction Problem 16.1 (Equilateral Triangle on a Given Segment.)

In hyperbolic geometry:

Theorem 19.4 (Uniqueness of Common Perpendiculars)

Some problems on the exam will just involve giving definitions. Here is a list of definitions you are responsible for knowing.

Chapter 8:

Polygon, convex polygon, congruence of polygons, semiparallel rays, chord of a polygon, interior and exterior of convex and non-convex polygons.

Chapter 9:

Quadrilateral, trapezoid, parallelogram, rhombus, rectangle, square

Chapter 10:

Angle sum of a polygon. The Euclidean Parallel Postulate.

Chapter 11:

Nonoverlapping regions, admissible decomposition,

Chapter 12:

Similarity, Cevian, golden ratio, golden rectangle

Chapter 13:

Sine, cosine

Chapter 14:

Circle, radius, chord, diameter, concentric, interior and exterior of a circle, secant line, tangent line, minor arc, semicircle, major arc, arc measure, angle inscribed in an arc, arc intercepted by an angle, tangential polygon, cyclic polygon.

Chapter 16:

Know the allowable operations that can be performed with compass and straightedge.

Chapter 17:

Defect of a polygon

Chapter 18:

Saccheri quadrilateral, Lambert quadrilateral, asymptotic rays

You will be given a list of theorems to reference. As usual, you may only use theorems from the book that come before the theorem you are trying to prove. The exception is the Pythagorean theorem: You may follow the proof in the book that uses Theorem 13.8/Theorem 13.9 (Right Triangle Similarity).

It is not necessary to refer to each theorem by number, so if you know a theorem is applicable you do not need to look it up.