Math 444 Class Notes

Monday 9/29/2003

• Axiomatic Approach to Geometry
• Birkhoff's Axioms (congruence SAS, high school version). These axioms only include SAS for congruence, not similarity, so they are not yet complete. Similarity will be discussed in Week 2.
• Properties of Isosceles Triangles

10/1/2003

• Kite Properties Proved
• SSS congruence criterion

10/3/2003

• If And Only If statements and Locus terminology
• Inequalities in Triangles - Vertical Angles, Exterior Angle Theorem, Greater-Angle-Greater Side
• Triangle Inequality
• Summary of Triangle Congruence Criteria -- SAS, SSS, ASA, HL

Monday 10/6/2003

• Answers to Class Exercise on Rul

10/10/2003

• Dilation Axiom
• Similarity Criteria for Triangles

10/15/2003

• Similar triangles with shared angle - the upside down case
• Tests for similar triangles

11/03/2003

• Cube in Class
• Cavalieri Links

11/14/2003

• Affine Plane Coordinates

11/17/2003

• Math in Barycentric Battleship

11/26/2003

• Transformation Classnotes
• Orbits

12/01/2003

• Compostion I (known)
• Composition II (new)
• Example of composition of two rotations

12/03/2003

• Translations and Glide Reflections
• Triple Line Reflection

12/05/2003

• Orientaton of Products of Isometries -- as easy as 2+3!
• Tables of Fixed Points and Invariant Lines
• Constructing Isometries from Images of Triangles and Segments
• Napoleon Proof and Fermat Point Proof

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