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Honors Geometry
Geometry Theorem In-Class Assignment (40 points)
For this assignment, you will research a theorem, problem or topic that we have not studied this
semester. In a group of two or three, you and your partners will find a topic on the internet, in
another geometry book, or even in our own book and research it. You will then create a presentation
on your topic and discuss it in class on Friday. Your presentation should include a Geometer’s
Sketchpad design illustrating the theorem. You should turn in a short, one- or two-page typed
summary of the topic and any interesting history behind it (including the history of the creator), in
addition to a printout of your GSP or TI-Nspire sketch. You must cite at least two sources
(Wikipeadia cannot be used as a source.) Remember to follow copyright law and provide
appropriate documentation of sources.
Some ideas for possible theorems/ projects for study:
(Note: In a class, no two groups may study the same theorem/problem/project)
Aubel’s Theorem
Blashke’s Theorem
Jung’s Theorem
Johnson’s Theorem
Kepler-Poinsat polyhedra
Koch’s snowflake vs Sierpinski’s
Lebesque’s minimal problem
Limacon of Pascal
Malfatti’s Problem
Poincare’s model of hyperbolic geometry
Plateau’s problem (use soap bubbles)
Seven circles Theorem
Steiner’s Theorem
Philo’s Line
Peaucellier’s cell (linkage strips)
Monge’s Theorem
Miquel’s Theorem
Penrose tilings
Blanche Descarte’s Division of a Square
Holditch’s Theorem
Cycloid by Mersenne
“Flatland” by Edwin A Abbott
taxicab geometry
spherical geometry
A theorem of your own choice, with instructor approval.
Guidelines for presentations:
 Your presentation should be aimed at another geometry student who knows nothing about the
topic. Define unfamiliar terms, for example, do not assume everyone knows what a “medial
triangle” is.
 Begin your group presentation with a brief summary of your work on the investigation.
(What is it about? What is the main point of the theorem?)
 Your GSP sketch should be a “good” sketch that if moved around, still shows the theorem is
true.
 Be sure that each member of the group participates in the presentation.
 Individual students in the group will receive a grade for the individual parts of the
presentation.
Honors Geometry
Geometry Theorem In-Class Assignment (40 points)
Grading Standards:
Organization
Is the presentation organized? Did you make the group familiar with the topic?
Content
Was the information correct? Did the speaker include clear diagrams as
needed? Did the speaker answer questions (if any) correctly?
Clarity
Did the audience understand what the speaker was talking about? Did the
speaker add explanations and examples when necessary?
Delivery
Was the presentation interesting?
Each component will receive a score of 5-0 for a total of 20 points for the presentation.
5:
Exemplary response (Did a great job)
4:
Competent response (Did a good job)
3:
Emerging (Almost; a fair job)
2:
Not effective (Not quite, but they tried)
1:
Minimal attempt (Not much effort given to topic)
0:
No attempt (Did not even try)
Your summary report and sketchpad printout will be worth 20 points each and will be graded based
upon:
The information is correctly illustrated. (6 points each)
The information is organized and labeled in a clear manner. (6 points each)
Printout of Geometer’s Sketchpad or Ti-Nspire sketches are included. (4 points)
There are no spelling or grammar errors. (4 points maximum deduction)
Honors Geometry
Geometry Theorem In-Class Assignment (40 points)
Honors Geometry
Theorem Presentation
Names:
Theorem:
Organization
Content
Clarity
Delivery
Total:
/20
Grading Standards:
Organization
Is the presentation organized? Did you make the group familiar with the topic?
Content
Was the information correct? Did the speaker include clear diagrams as
needed? Did the speaker answer questions (if any) correctly?
Clarity
Did the audience understand what the speaker was talking about? Did the
speaker add explanations and examples when necessary?
Delivery
Was the presentation interesting?
Each component will receive a score of 5-0 for a total of 20 points for the presentation.
5:
Exemplary response (Did a great job)
4:
Competent response (Did a good job)
3:
Emerging (Almost; a fair job)
2:
Not effective (Not quite, but they tried)
1:
Minimal attempt (Not much effort given to topic)
0:
No attempt (Did not even try)