Euclidean Geometry
(Essential Elements)

SSS Failure
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What is Correspondence
Isometry
Side-Side-Side
Bisecting Angles
Side Angle Side
Angle-Side-Angle
Isoceles
Right Bisector Construction, Etc.
Perpendicular - Point to Line
SSS Failure
SAS Failure
ASA Failure
Parallel Lines
Angle Sum
Similarity
Right Triangle Similarity
Trig  or Similarity
Parallelograms
Kites From Triangles Duplication
Parallelogram from Triangle Duplication

 Deductive logic in maths may begin
  here.  But deductive   logic mastery 
itself  may begin with words and stories.

Complex Numbers
Update (December 13th, 2009). A
simpler & quicker development of 
complex numbers  is  available: 

When do Triangle Construction Methods fail?

Success and Failure of the SSS method.

The sum of lengths of any two sides in a triangle is greater than the third.  The side-side-side  ruler and compass (or string) triangle construction method fails when the sum of the shorter two lengths b and c is less than the longest a. See figure.

Here there is no intersection of the circles centered at the ends of the longest length. So the side-side-side construction method fails.

Side-Side-Side triangle construction methods works when the the length of  longest side is less than the sum of the lengths of the other two sides.

The two intersections of the circles centered at the endpoint o the base length a, each give provide a vertex of a triangle with the given lengths a, b and c.

www.whyslopes.com

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Parents: Help your Child/Teen Learn covers  Speaking Skills, Reading & Writing,  Preparing for Science &  Having Patience, etc

Math How-TOs
1. Arithmetic   2. Algebra   3.  More Algebra  4.  Geometry 5 More Geometry 6.  Calculus
>> densely written 
>> use as skill checklists

Online Volumes (orders)
1,  Elements of Reason. 1996
1A. Pattern Based Reason  1995
1B. Math Curriculum Notes 1996
2. Three Skills for Algebra  1995
3 .Why.Slopes.&.More.Math.1995

Skill & Concept 
Review or  Development 

 1. Decimal Arith - Video Based ]
2   Fractions  
3.  Fractions  with Units  
3. Solving Linear Equations  - 
making alg easier
4. Formulas forwards & Backwards - unifying theme for Algebra
5.  Proportionality, Back- & For-wards - theme at work.
6.  Logic - Math Free, good for precision in  work & studies 
7. Euclidean-Geometry  (leanly)
8. Slopes and Lines 
9. Why Study Slopes - a context 
10.  Quadratics
11  Polynomials
12  Factored Polys - a context
13 Functions - For-& Back -wards
14  Number Theory, Richly
15. Exponents, Radicals & logs.  
16   Calculus - Examples & Advice 
17.   Real  Analysis 
18  Electric Circuits Etc (So So)
19 Maps, Similarity & Trig, (alt view)
20 Complex numbers  
21 Logic with Symbols+truth tables
22  Consistent Story Telling
23. Even More Logic