Welcome to the Geometry Zone

(Geometry, Periods A and F)
Web address shortcut for this page: www.modd.net/78geom

Are you nervous when you see NCWEE? concerned when you see CIRC? perturbed when you see PBC? Visit Mr. Hansen’s fabled abbreviations page to make sense of those cryptic markings you see on your papers.


Schedule at a Glance (see archives for older entries)
Written assignments should follow the HW guidelines.


M 5/19/08

Test (100 pts.) on §15.3 (Hinge Theorem) and §§9.9-9.10 (trigonometry and inverse trigonometry).


T 5/20/08

Field trip to the National Cryptologic Museum, Fort Meade, MD. Bus will depart at 8:00 a.m. Bus will probably be loading in the area near Satterlee-Henderson Field, but stay alert and try not to miss the bus! Attendance will be taken. If you attend the field trip, you are excused from A through E periods and the first half of F period. If you do not attend the field trip, you must attend all your classes. F period geometry class will probably start about 10 minutes late, at approximately 12:45.


W 5/21/08

Review for final exam.


Th 5/22/08

Review for final exam.


F 5/23/08

Last day of school/wrap-up.


M 6/2/08

Final Exam, 8:00–10:00 a.m., Lower School Music Room.

Bring the following materials with you:


  • Several sharpened pencils
  • Straightedge (optional)
  • Compass (optional)
  • Index card with your name on it. You may write up to 5 formulas on your index card. For example, you may wish to write the following:


Do not bring notes, scratch paper, cell phones, calculators, or other electronic devices into the exam room with you.


The exam covers chapters 8 through 15, as well as the basic supporting facts from the first semester. For example, you cannot forget what the words “complementary” and “supplementary” mean, even though those topics were covered and tested in the first semester. When preparing for the exam, it should be sufficient to focus on the chapter summaries and chapter review questions at the end of chapters 8 through 15. Format of the exam will be as follows:


  • Multiple choice: 50 to 60 questions with no additional penalty for wrong guesses. Each question will be worth approximately 1.5% of your exam grade. Therefore, if you cannot solve a problem, you should simply skip it and come back to it later if time permits.
  • Procedural essay (10% of exam grade). For example, you may be asked to describe how to construct an equilateral triangle, or you may be asked to describe how to determine all the possible loci created when a certain type of locus or figure is intersected with another type of locus or figure. Merely giving the answer is not sufficient. In order to qualify for full credit, you must describe the process that you go through in order to solve the problem. See example below.
  • Coordinate geometry proof (10% of exam grade). You must set up an xy-plane with coordinate grid and create a diagram, without loss of generality, in order to demonstrate the validity of a proposed statement. See example below.


Example Multiple-Choice Question. Choose the letter of the best answer.


1. A young person is standing on level ground 6 feet from the base of a 10-foot lamppost on a sunny day. The angle of the sun is such that the shadow cast by the top of the young person’s head exactly coincides (on the ground) with the shadow cast by the tip of the lamppost at a point that is 22 feet from the base of the lamppost and 16 feet from the young person’s foot. How tall is the young person?

(A)  feet

(B)  feet

(C)  feet

(D)  feet

(E) Insufficient information. Either (A) or (C) could be correct, depending on which side of the lamppost the sun is located with respect to the young person.


Work the problem and commit yourself to an answer, and then check your answer against the solution key below.


Example Procedural Essay Question. You may abbreviate, and sentence fragments are permitted. However, misspellings and blatant grammatical or wording errors may result in point deductions.


2. Explain how the principle of compound locus allows one to find the circumcenter of any triangle.


Example Coordinate Geometry Proof.


3. Prove that the diagonals of an isosceles trapezoid cross in such a way that two isosceles triangles are formed, one for each base. (You may assume that with an isosceles trapezoid, the longer base protrudes from the shorter base by an equal length on each side. This property is a consequence of the fact that the diagonals are congruent.)


After you have made a reasonable effort to solve all three problems on your own, click here to see the solutions. Warning: Do not peek before you have tried to solve the problems with pencil and paper. Otherwise, you are simply deluding yourself.


Fun Links:
-- New world record for paper folding! Pomona, CA, teenager achieves a seemingly impossible 12 folds!
-- Lots and lots of
online IQ tests
Fallacious proof that pi equals 5
-- An extension of the concept of
freshman cancellation
National Cryptologic Museum, brought to you by the National Security Agency
-- The famous three houses/three utilities puzzle
-- The amazing nine-point circle
-- Abusive tax shelters: Maybe you will use your education to devise clever schemes like this, or better yet, to try to eliminate them
More fun links on Mr. Hansen’s home page

Study-Related Links:
-- Midterm exam study guide and practice exam
-- Angle-arc puzzles written by the Class of 2006 (in 2003)
-- More angle-arc puzzles written by the Class of 2007 (in 2004)
-- Brain teasers written by the Class of 2008 (in 2004-05)
-- Timed math quizzes, courtesy of Mr. Errett
Quizzes, quizzes, and more quizzes for geometry and other math subjects (don’t let the title ‘Math for Morons’ discourage you—that’s really a moronic name for the site)
-- Proficiency test for rising 9th graders from the great state of Illinois
-- B.J. Pinchbeck’s
Homework Helper for all subjects
-- Practice test: Chapter 1

Serious Links (click here)

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Last updated: 29 May 2008