Euclidean Geometry
(Essential Elements)

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
(August 20, 2008) 

Addition of points in the plane
Multiplication of Points in the Plane
Distributive Law, Step I
Distributive Law, Step II
Distributive Law, Step III

The exposition of complex numbers
here has the same level of  applied
mathematics rigour as the development 
of trig via the drawing of right triangles
and unit circles.

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

Would you like to show yourself or others how to be  algebra power users?

Isosceles Triangles

A triangle is said to be isosceles if 

1. Two sides in it have equal length, or 
2. Two angles in it are equal. 

The next two theorems show that the conditions (1) and (2) are equivalent. That is, each implies the other. 

Digression: To encourage further site exploration, here are two site descriptions 

• Math Forum, 1996 online classification of the then  dozen or so math lesson giving  websites: ... There are appetizers for algebra, arithmetic, logic, better learning in general, reason, theorem proving and complex numbers.  Strengths here are in Alan's explanation of mathematical concepts using words and stories: ...     
  
• Magellan, the McKinley Internet Directory, 1996: Mathphobics, this site may ease your fears of the subject, perhaps even help you enjoy it. The tone of the little lessons and "appetizers" on math and logic is unintimidating, sometimes funny and very clear. There are a number of different angles offered, and you do not need to follow any linear lesson plan. Just pick and peck. The site also offers some reflections on teaching, so that teachers can not only use the site as part of their lesson, but also learn from it.

Where there is smoke, there is fire.  Bon Appetite.

Theorem 1. If  two sides in a triangle have equal lengths then the angles opposite them are equal.

Proof of theorem 1: 

 

  
Click on thumbnail to see proof.

Theorem 2. If two angles in a triangle are equal then the sides opposite them have equal length.

Proof of theorem 2: 

   

Click on thumbnail to see proof.

Equilateral and Equiangular Triangles

A triangle is said to be equilateral when and only when all three sides in it have the same length.  A triangle is said to be equiangular when and only when all three angles in it are equal.

Theorems 1 and 2 above imply the following.

Theorem 3. A triangle is equilateral when and only when it is equiangular.

www.whyslopes.com

Parents: Help your Child/Teen Learn

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

Math How-TOs etc  2008
1. Arithmetic
2. Algebra 
3. More Algebra 
4. Geometry  
5. More Geometry
6. Calculus

Site Description/Reviews  by 3rd parties

Site  Math Lessons
1. Arithmetic Flash Videos  11-2008
2.  Algebra Videos (to appear)
3. Fractions and More 
4..  Solving Linear Equations  04-2005
5. Euclidean-Geometry To Complex No.s 
6.  Analytic Geometry/Functions 2006
7.  Number Theory. 2006-7
8.  Exponents, Radicals & logs. 2008
9 Calculus  2005
10..Real  Analysis 1995
11 Electric Circuits Etc  2007
12. .Algebra, Odds & Ends, HS level-2001

For Math Instructors/Tutors/
Curriculum Committees

1. K0-11Applied Math Program Outline  
2. Mathematics education  essays 
3. LAMP - an earlier applied math program.
4. Maps, Plans,  Similarity &Trig, with
Complex   Numbers, 12-2009. (150 pages)

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Visitors:  Ask a question by email if you cannot find what you need in www.whyslopes.com  for high school or college maths courses - answers will be added to site content.