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M
11/3/03
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HW due:
Write §4.4 #1, 2, 9, 12, 13, 16. Also, practice constructing ^ bisectors so that you can make a clean one today (Monday)
using compass and straightedge. If you missed the rather hurried explanation
given at the end of class Friday, here
is a better explanation.
After school, I will be in Math Lab even though there is a faculty meeting.
(Mr. Kelley asked me to staff the room since because students in other
classes have tests tomorrow.) There are also links posted below to help you
with your constructions if you are still feeling shaky.
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T
11/4/03
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HW due:
Fill out the PBT Mastery Quiz
and bring it to class with you. Also make three (3) random triangles, and use
the principles of PBCC, ABIC, and MCCG to construct the circumcenter (and
circumscribed circle) of the first triangle, the incenter (and inscribed
circle) of the second triangle, and the centroid of the third triangle.
PBCC Û perpendicular
bisectors meet at the circumcenter
ABIC Û angle bisectors meet
at the incenter
MCCG Û medians meet at the
centroid (a.k.a. center of gravity if triangular region is of uniform
density)
We learned how to perform the following using compass and straightedge:
When performing your constructions, try to be neat (start over if
necessary—paper is cheap). Remember that “bigger is better,” since larger
diagrams tend to have smaller percentage errors. Show your arc marks clearly.
If you do not have a compass, please make a note to buy one as soon as you
can, and use your “compass fingers” until then.
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W
11/5/03
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HW due:
Read §4.5; write §4.5 #1, 2, 3; write §4.6 #1, 4, 6, 8, 9, 11. Also, redo
your ABIC (inscribed circle) construction. Make it good and large, with the
radius of the inscribed circle constructed using the manner described in
class. (If point I is the incenter, construct a perpendicular segment from I
to one of the sides of the triangle, and use that segment’s length as the
radius.)
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Th
11/6/03
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HW due:
Read §5.1 and write an indirect paragraph proof of the following theorem:
“If a person is able to type 120 words per minute without making any typographical
errors, while simultaneously speaking a foreign language and playing piano
with his feet, then that person is not inebriated.”
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F
11/7/03
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Both classes (A and B period) will meet in Steuart
202 today.
HW due: §5.1 #2, 5, 10, 11, 12. Please
also take a look at the amazing nine point circle. It is a
bit difficult to construct with pencil and paper, but it is a snap with
Geometer’s Sketchpad.
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M
11/10/03
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Quiz (50 points) on Chapter 4 and Constructions.
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T
11/11/03
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HW due: Do
35 minutes’ worth of review problems from the end of Chapter 4.
In class: Q&A/review for test.
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W
11/12/03
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Test on Chapter 4 and Constructions.
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Th
11/13/03
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HW due:
Read §5.2; write §5.2 #1-6 all, 8, 9, 11.
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F
11/14/03
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Happy Quiz
(counts only if it helps your average) on §§5.1 and 5.2.
HW due: Read §5.3 and put
abbreviations for theorems 31-44 either in your reading notes or in the
margin of your textbook on p.743; write §5.3 #1, 10, 29.
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M
11/17/03
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HW due:
Write §5.3 #16, 17, 18 (omit diagram), 20, 22, 28, 30. If, after giving #30 a
good solid try, you are unable to make any progress, you may copy the proof from
p. 295. Placeholders will not be accepted for problem #30 even if your time
log is complete.
For #29, which is carried over from Friday, you need to demonstrate attempts
and blind alleys if your proof is incomplete. You may not count this work
toward your 35-minute target for today. If you had a placeholder or an
obviously incomplete proof on Friday, that will not qualify for credit today.
Also note for #29: Although a proof by similarity is valid, that uses
techniques from Chapter 8 that we have not formally established yet. Please
use only the theorems that have been developed in the textbook up to this
point. Hint: Add auxiliary line DF.
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T
11/18/03
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HW due:
Read several times through the Construction
of the Nine-Point Circle. You may also enjoy seeing the interactive animation. Make
yourself a nine-point circle cheat sheet (this will be graded) so that when
you come to class you can construct your own nine-point circle: all nine
points plus the center and radius of the circle itself. Also print out Sketchpad Lab III and bring it to class to
work on.
In class, you will use your cheat sheet to construct the nine-point circle
two ways:
1. First, you will use compass and
straightedge and will construct the center of the nine-point circle by
the simpler method (i.e., by finding the circumcenter of the “triangle of
midpoints”).
2. Then, you will use Geometer’s
Sketchpad to construct the center of the nine-point circle by the more
complicated method (i.e., by finding the midpoint between the orthocenter and
circumcenter of the original triangle).
Note: Although construction of the
nine-point circle will be on your next test, you may save your cheat sheet
for use on tests and quizzes.
Bonus (optional HW, 3 points):
Prove the result that we called Mautner’s Lemma
and its converse. Remember, when we first encountered this, we did not
have enough tools to prove the lemma. I tried for quite a while, but I was
unable to come up with a proof that relied only upon things we knew at that
point. But now you may try again!
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W
11/19/03
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HW due: Mautner’s Lemma and its converse. Use the hint
that we discussed in class on Tuesday. Since nobody had this correct, we will
carry this over to tomorrow with an additional hint (see below).
HW due at end of class: Sketchpad Lab
III and the two nine-point circle constructions. See entry for 11/18 to
see the two methods of constructing the center of the nine-point circle.
If you finish early, you may play Geometry Jeopardy Bingo or leave class
early.
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Th
11/20/03
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HW due:
Read §5.4; write §5.4 #15, 17, and use a pencil
to fill in all the columns of the Polygon
Feature Chart.
Additional HW due: Mautner’s Lemma and its converse. An
additional hint is to label the intersection of the medians as point P, and
focus on lengths MP and NP. What happens if MP = NP? What happens if MP ¹ NP?
Sketchpad Lab III and the two
nine-point circle constructions will be accepted without penalty until 3:00
p.m. today.
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F
11/21/03
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Note: Both classes will meet in Steuart 202
today.
Quiz on §§5.1 through 5.3 and nine-point circles. You may use your cheat sheet, provided that it is handwritten in your own writing. You
may manually copy a friend’s cheat sheet if you wish, but no photocopies or
computer output will be permitted.
HW due: Read §5.5 and use it to correct your Polygon Feature Chart. Also write
§5.5 #9, 18. (For each of these, write a diagram, “givens,” “prove,” and a
2-column proof.) Finally, answer the following questions:
1. Let ABCD be a parallelogram that is not a rhombus. Do the diagonals of
ABCD bisect the angles?
2. If your answer to #1 is “yes,” make a diagram that proves this is
possible. If your answer to #1 is “no,” provide a short proof by
contradiction.
The following additional column of answers (for the column concerning the
“aabb” pattern for Ðs) is provided to help you fill in your Polygon Feature Chart:
Quadrilateral: sometimes
Convex Quadrilateral: sometimes
Parallel-O-Gram: sometimes (footnote r)
Rectangle: always
Rhombus: sometimes (footnote s)
Kite: sometimes (footnote s)
Square: always
Trapezoid: sometimes (footnote i)
Isosceles Trapezoid: always
Triangle: never
Isosceles Triangle: never
Equilateral Triangle: never
Bonus HW due (4 points): Mautner’s Lemma and its converse. Since nobody
has solved this yet, here are some final hints that should allow you to make
good progress:
1. Let P be the intersection of the medians. Show that if MP = NP, then
eventually the lemma works out.
2. Show that if MP < NP, then you eventually reach a contradiction.
3. Show that if MP > NP, then a situation analagous to hint #2 occurs. Or,
you can make a wlog assertion if you explain your reasoning.
4. Combine hints 1, 2, and 3 to make a complete proof.
5. The converse of the lemma is straightforward, by SAS. Start here if you
can’t do anything else.
Easier Bonus HW due (2 points):
Solve the Bricklayer vs. Architect
brainteaser.
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M
11/24/03
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HW due:
§5.6 #4 (answers only), 5, 6, 10, 11, 13.
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T
11/25/03
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Note: Both classes will meet in Steuart 202
today.
HW due: §5.7 #2, 10, 13, 14, 16,
17. Also, do the optional Happy
Homework (up to 4 pts. bonus) by re-doing all
of last Friday’s quiz. Use the version posted, do the entire quiz, and show your work.
Q. Mr. Hansen, may we compare answers with our friends?
A. Yes, but only to check to see if your answers agree after you have worked the problems.
Q. Are we allowed to copy their work, too?
A. No. Your work must be your own. To copy somebody else’s work would be an
honor code violation.
Q. Are we allowed to get a list of correct answers and then work toward
those?
A. No. You may check answers only after you have worked the problems on your
own.
If the class homework survey goes well (i.e., if everyone has essentially
correct work, or work that can be patched up while we are going through the
answers), we will watch a video and will play Geometry Jeopardy Bingo
afterward.
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W
11/26/03
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No school (Thanksgiving
break).
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