Final Exam: Your Geometry Portfolio

Directions
What Mr. Kowal Knows
When working and writing your solutions to the exercises I’ve posted you need to assume that I do not know anything about Geometry. In fact, the only thing you can assume that I do know is the following:

1. I know what lines, segments, points, rays, and angles are
2. I know what an “opposite side” is
3. I know what non-common sides are
4. I know that angles are measured in degrees
5. I know that if two lines intersect the angles formed by the two pairs of opposite rays make ONE 90 degree angle. I do not understand if more right angles may exist; you need to prove this fact

In addition to my limited knowledge as a teacher of Geometry I have a weird condition of amnesia. You see, when I read a proof of yours I do not remember anything you have proved once I finish reading it. Because of this condition, if you think I remember or know some fact that you have proved in one exercise I DON’T- you need to re-prove everything in your subsequent examples.

What Mr. Kowal’s Students Know
Here is a list of definitions and two theorems you know if you had Mr. Kowal as a student in Geometry:

1. You know everything that I know above.
2. You know the definition of Vertical Angles
3. You know the definition of a Linear Pair
4. You know what corresponding, alternate interior/exterior angles are
5. You know that given two lines that are cut by a transversal that

-if alternate interior angles are congruent, or alternate exterior angles are congruent, or corresponding angles are congruent then the two lines that are cut by the transversal are parallel

-likewise, if the two lines that are cut by the transversal are parallel then alternate interior angles are congruent, or alternate exterior angles are congruent, or corresponding angles are congruent.

The only condition in stating that objects are a linear pair, vertical angles, etc. is that you have to show me that the necessary conditions exist in order to give rise to mathematical object's existence. For instance, if you say that two angles are a linear pair then you better show me that there exists two angles whose non-common sides form opposite rays; if you do not then I will ask why and deduct points.

I have provided an example of how a student proved #43 on pg. 160. It is posted below. The student’s work is perfect. Notice how he shows the existence of every geometric object instead of just stating that angles are a linear pair or lines are parallel. Your proofs need to model this example if you want full credit.

Organization of Your Portfolio:

In order to receive full credit then your work must be assembled in the following manner:

1. Only one proof per page. ALL PROOFS WRITTEN IN PARAGRAPH FORMAT like the example provided below #43 pg.160
2. Use only copy paper.
3. Draw any pictures that I give you on your proofs so I can follow what you are saying about the picture when I read your proof.
4. Staple all of your proofs together and then staple, separately, all of your NAF Quizzes. I will not have a stapler in class Monday.
5. Put your name on all of your work.
6. Place all of your work in a manila folder.
7. Your portfolio is due Monday morning at 7:45. I will be in our classroom at this time. Turning the portfolio in late will make you lose points.