Assignment 6 (Due Wed 11/2)

This assignment has two parts. Part A is a big problem about a ski cabin. You can, and are encouraged to work on this with another student and turn it in a joint work that you both sign. Since it is lengthy, it is important that your work be even more readable and even better organized than usual. Include enough explanation that a person who was not familar with the problem could follow your reasoning.

Part A: Ski Cabin Problem

Problem 6.1 (do this with a partner if you like) Follow this link to the Ski Cabin Problem.

Part B. Greatest Hits from Old Test

Part B has problems from tests given in 444 in the past.You should find this helpful in your test preparation. For these problems, the usual custom applies. You can consult other students, as usual, but write up your own answers independently.

Problem 6.2 (from Quiz 1, 2004 -- follow the link for other questions on this quiz)

• Prove that a quadrilateral EFGH is a parallelogram if and only if its opposite angles are congruent (i.e., angle E = angle G and angle F = angle H). Note:  You can use any theorems (including theorems about parallel lines) except theorems about parallelograms (which you must prove as part of your proof).

Problem 6.3 (from Quiz 1, 2003 follow the link for other questions on this quiz) - Zigzag Problem

In this figure, E is on line AC and D is on line AB, and angles ABC, ACD, and ADE are right angles.  Length |AB| = 4 and |AC| = 5 Compute an exact numerical value (i.e., not a decimal approximation) for the lengths of the following segments. Show your reasoning clearly enough to follow, but THIS DOES NOT HAVE TO BE ORGANIZED AND JUSTIFIED AS A FORMAL PROOF; it is problem solving. AD __________ AE __________ BC __________ CD __________

Problem 6.4 Do Problem 1 from the 2004 Midterm (at this link)

Problem 6.5 Do Problem 2 from the 2004 Midterm (at this link)