Math 412:Geometry II

Finals week: I will be around Tuesday 9-3 and Wednesday 11-3 (with a break for lunch somewhere in the middle) to answer questions. The final is Thursday at 1:00 in the computer lab.

Monday Wednesday Friday

Jan 26 Introductions. Patty paper investigation. Isosceles triangle problems

Assn: Read/watch about Van Hiele levels
Do and reflect on sec 4.2 # 2, 4, 6, 7
Look at section 2.5 & 2.6 (know the conjectures)
Tell me 2-3 things you particularly want to do. You can look in the book, or follow the links below.

Discussion of reasoning from isosceles triangle problems

Angles, angle sum and triangle congruence theorems

Assn: do and reflect on sec 4.3 # 12, 13
4.4 # 1-6, 9-14
Post Geometry topics that look interesting to the D2L Discussion board.

Flow chart proofs; scaffolding for proof.

Discussion of Van Hiele levels

Feb 2 Flow chart vs two column proofs
Elementary Ed opportunity:
Montessori Education: Hands On presentation by Gay Ward and Kathy Tomlinson. (at the River Falls Academy Gym on Mon. Feb. 2nd from 6:30 - 8 pm). This is a free presentation where Montessori math (and other subject) materials will be shared. Cool stuff
Here's a map

Discussions of proofs, and ways to support learning proof reasoning

Discuss the role of proof in geometry
Feb 9 Concurrency: sec 3.7


Concurrency: Centroid sec 3.8
Points of concurrency Applet


Van Hiele level 2 arguments,
Miquel and Appolonius


Feb 16 polygon angle sum 5.1

A file

Kites and trapezoids 5.3


Venn diagrams and quadrilaterals

Feb 23midsegments 5.4


Chords 6.1


Tangent lines 6.2


March 2 . Arcs and angles 6.3



 Circumference and arc length 6.5


"Power" of a point Worksheet probs.
Also do: Write a problem similar and solve for:
5.1 # 5, 7, 8
5.2 # 2, 5, 6
5.3 # 2, 5, 7, 8
5.4 # 5, 6, 7, 8

Mar 9 TBA star polygons  Midterm
Spring Break    
Mar 23 Transformations and symmetry

tessellations 7.4


more tessellations 7.5


Mar 30 still more tessellations 7.6


composition of transformations 7.3


Area review

April 6 Area of reg polygons 8.4


Circle area 8.5


Surface area 8.7


April 13 Pythagorean Theorem 9.1


Pythagorean theorem and circles 9.6



Apr 20 A problem of definitions: 3D shapes

Platonic solids & Euler's formula



More Euler


Apr 27 more about composition of transformations

more euler 3D shapes as shadows
May 4 surface area and isometric drawings Similarity as scale factor with area  

  Some topics that may be substituted in to replace other topics:

Self similar fractals for example

Star polygons for example

semi-regular tessellations for example

Conway tessellations (this is in the book--tessellations of Conway hexagons)

Pick's formula for example

platonic solids for example

duals of solids for example

3D shapes from shadows for example

Euler number, etc. see here and here

Symbolic logic This is in the book.

Miquel's theorem for example

basic symmetry groups for example

Wallpaper patterns/groups for example

Ceva's theorem (and Menelaus?) for example

Morley's thm for example

Trisection and paper folding see here, here and here

Symmedians for example

Linkages see here or here