Schedule for MAT515, Fall 2020
topics for dates in the future are estimated

Week Monday Wednesday Reading and Assignments
8/24 Administrivia
General discussion about teaching geometry; numbers and number lines

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Lines, Parallels, and Betweenness

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We can assume students know about rational numbers and the number line
or see section 1.1 definition of a fraction

Please read "To the Pre-Service Teacher" in the frontmatter from the text.
Also, we covered most of section 4.1 basic vocabulary.
8/31 Polygons, Separation, Convexity.

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Distance, Angles, and Angle measure.

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section 4.2 basic vocabulary, part 2. See also A Characterization of Regular Polygons.

Homework 01, due Wed. 9/9. Here are the solutions.
9/7 Labor Day holiday Circles, Polygonal regions, Transformations of the plane

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section 4.3 transformations of the plane.

Homework 02, due Wed. 9/16. Here are the solutions, still in progress.
9/14 Transformations: Rotations

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Reflections and Translations

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section 4.4 Rotations, and section 4.5 Reflections and Translations

Homework 03, due Wed. 9/23. Here are the solutions.
9/21 Congruence: SAS and ASA

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Proof of ASA & Fundamental Theorem of Similarity

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section 4.6 Congruence, SAS, and ASA, section 4.7 A brief pedagogical discussion, and section 5.1 The Fundamental Theorem of Similarity.

Homework 04, due Wed. 9/30. Here are the solutions
9/28 more FTS, Dilations

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Dilations and Similarity

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section 5.2 Dilations and section 5.3 Dilation and Similarity. See also this Theorem about Similarity.
Also, you might find this list of axioms and theorems helpful.

Homework 05, due Wed. 10/7. Here are the solutions.
10/5 Similarity, Pythagorean theorem

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SSS and its consequences

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You might want to look at this video of the proof in the text and/or more than 120 proofs of the Pythagorean Theorem.
NOTE: We will now be using the published textbook, so I will not be posting extracts any longer.
Section 6.1 Review, Section 6.2 SSS and consequences, and Section 6.3 Pedagogical comments.

Homework 06, due Wed. 10/14. Here are the solutions
10/12 Proof of FTS

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The angle sum of a triangle

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Section 6.4 Proof of FTS, see also The proof of FTS for r real.
Section 6.5 The angle sum of a triangle.

Homework 07, due Wed. 10/21. Here are the solutions.
10/19 Triangle inequality and characterization of isometries.

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Triangle centers: Circumcenter, Orthocenter, Centriod, and Incenter

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Section 6.6 Characterization of isometries
Section 6.7 Properties of triangles.

No homework due on 10/28
10/26 Problem session/review

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Midterm exam, on 10/28 from 6pm-7:25, in person.

Here is the midterm, and here are the solutions.
11/2 The Euler line

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Theorems of Ceva and Menalaus.

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Section 6.7 Properties of triangles

Homework 8, due Wed. 11/11 and here are the solutions.
11/9 Circles

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More about Circles

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Section 6.8 Properties of circles

Homework 9, due Wed. 11/18. And here are the solutions.
11/16 Even More Circles

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The Power of a point and the radical axis, the Miquel point, and the 9-point Circle.

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Section 6.9 The power of a point
Section 6.10 Two theorems about circles
11/23
Thanksgiving Break
Homework: eat lots of pie! (real, actual pie, not McDonald's "pie")
11/30 Class cancelled due to family reasons. Straightedge and Compass constructions

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chapter 7 Ruler and Compass Constructions
12/7 Optional class (no new material) Final exam
due Wed, December 9

Here is the final exam.

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Last modified on Mon, 7 Dec 2020 at 10:52am