Math 445 Assignment 5

Math 445 Assignment 5
Reminder: QUIZ #2 is Friday, 2/04/00

Reading

Read Chapter 3 in Sved (Dr. Whatif’s Euclidean Geometry).
You got a photocopied handout entitled Chapter 5. Euclidean Geometry. We will refer to this as EG.Read EG, Section 5.1. Also, we will begin Sved, Chapter 4 at the beginning of next week.
These problems will be done in class: EG, p. 5-4, #1, #2, p. 5-9 #1.

Assignment 5 (due Wed. 2/02/00)

Part 1. (55 points) Individual Problems.

(25 points) EG, p. 5-4 #4. This would be a lengthy problem, so we will break it up as follows. Each person will be assigned a subset of the propositions about which s/he should answer all the questions. Specifically for each of your propositions, restate the proposition in modern language and then answer in complete sentences whether it is (one of) the proposition(s) called for in (a) – (d) and answer (e) for your subset of propositions 35-45. If for (a) it is a construction, tell which one and how the construction is carried out. The individual assignments will be given by email and in a table at the bottom of this assignment..
(10 points) EG, p. 5-9 #2. Fill in the missing steps. Also construct (with straightedge and compass or Sketchpad) an accurate figure which shows why the "proof" goes astray. Where does this happen in the logical steps.
(10 points) EG, p. 5-10 #3. Construct an accurate figure with diameters BC and BD. Then tell what is really true in the figure and prove it.
(10 points) EG, p. 5-15 #1.

Part 2. (40 points) Do this with a partner.

(10 points) In the DWEG model, given points A, B and C. Construct with Sketchpad the (DWEG) line AB and the line through C perpendicular to line AB. Do the general case and also two extra constructions for special cases: one where A is the point at infinity and one where C is the point at infinity. Write a concise but clear explanation of the steps in the construction in the general case. Make this a script as described in the lab.
(10 points) Answer Sved, page 57, #4. Use this in the DWEG model, given points A and B, to construct with Sketchpad the (DWEG) circle through B with center A. Also do constructions where A or B is at infinity. Write a concise but clear explanation of the steps in the construction in the general case. Make this a script. This defines a DWEG compass tool.
(10 points) Use your DWEG compass and line tools to construct a DWEG equilateral triangle ABC, given points A and B. Save the sketch to turn in.
(10 points) Use your DWEG compass and line tools to construct a DWEG square ABCD, given points A and B. Save the sketch to turn in.