Euclidean Geometry (summer 2005) - geometry and trigonometry without coordinates. Master first

1. Correspondence between triangles. Here is an explicit definition, not always seen in class.
2. Isometry of Triangles - Here is a definition.
3. Side-Side-Side method
4. Side Angle Side method
5. Angle-Side-Angle method
6. Isoceles and Equilateral Triangles
7. Side-Side-Side Failure
8. SAS Failure or Near Failure
9. ASA Failure - links with the parallel postulate
10. Parallel Lines - and angles associated with a transversal.
11. Triangle Angle Sum - from the parallel postulate
12. Similarity and Minimal Conditions for
13. Right Angle Trig., from Similarity
14. Trig & Similarity - More about the Connection
15. Parallelograms and their Properties
16. Arrows and Vectors in the Plane

*Peer refinement welcome.t

he assumption of coordinates covering lines, planes and space connects geometry and algebra in the thought-based development of distance formula, vectors, complex numbers, unit-circle trigonometry. etc.

1. Real Numbers
2. Real No.s More
3. Linear Inequalities
4. Say More Positive
5. Rectangular Coords
6. Distance Formulas
7. Add & Multiply Points
8. Polar Coordinates
9. Radians
10. (A) Vectors
    (A) Coordinate Arithmetic
    (A) Navigation on Maps
    (A) Addition Geometrically
    (A) Rotation
11. (C) Complex Numbers
    (C) Distributive Law
    (C) Properties
    (C)  Complex Conjugates
    (C)  Pythagoras New Proof
12. (T) Unit Circle Trig
    (T) Complex Numbers &Trig
    (T) cis or exponential FNS
    (T) Dot & Cross Products
    (T) Cosine Law
    (T) Pythagoras Converse
13. (L)  Lines Slopes Equations
    (L)  Deriving Eq'ns
    (L)  Perpendicular
    (L)  Numerically
    (L)  3 Eqn Forms
    (L)  Algebraic View
    (L) System of Equations
    (L) Odds & Ends
14. (PT) Dilatations
    (PT) Translations
    (PT) Rotations
15. Quadratics
16. Conic Sections
17. (FN) Functions
    (FN) With Formulas
    (FN) With Sets
    (FN) Vertical Line Rule
    (FN) Horizontal Line Rule
    (FN) Inverse Functions
    (FN)  Why Sets
    (FN) Odds and Ends
18. Inequalities