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Logic 5 Chapters Arithmetic 10 Steps Algebra 12 Starter Steps & 5 Advanced Steps
Work & Study 23 Tips Geometry 15 Steps Calculus 70 Lessons

Ages 15+: Why study slopes Polynomials Quadratics Why factor polynomials Logarithms Functions
What is similarity Euclidean geometry leanly Coordinates + complex no.s Vectors DC Electric Circuits

Ages 14+: Prime factorization Written work formats Decimal place value Extend arithmetic skills orally
What is a variable 5 fraction operations by raising terms Solving Linear Equations: Take I Take II

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More Math, 1A - Pattern Based Reason, 1B - Skill Development Principles + Troubles
Forewords + leading chapters give original reasons, still valid, for site content & growth.

2 Euclidean Geometry Constructions Theory extras

Euclidean Geometry

Euclid about 300 BC in his elements produced a codification of geometry before the invention of coordinates by Renes Descartes 1800 year later. Knowledge of Geometry before coordinates may be employed in the development of geometry with coordinates.

This area on Euclidean Geometry on geometry before coordinates offers thought-based explanation of the following. Try to read them in sequence. There is more to Euclidean Geometry than this, but the following elements cover the least amount possible for the following site development of analytic geometry and trigonometry.

1. Common Terms and Vocubulary: Points, lines, rays, line segments.
2. Correspondence between triangles. Here is an explicit definition, not always seen in class.
3. Isometry of Triangles - Here is a definition.
4. Side-Side-Side (SSs) method for triangle construction and SSS like method for locating point.
5. Side Angle Side (SAS) method plus an application
   Ruler and Compass Construction to Bisect an Angle
6. Angle-Side-Angle (ASA)method, and ASA-like method for determining current location in navigation.
7. Isosceles and Equilateral Triangles plus applications: Construction and Characterization of a Right Bisector of a Line Segment and Ruler and Compass Construction of a Perpendicular from a Point to a line (with properties of such perpendiculars)
8. Side-Side-Side Failure
9. SAS Failure or Near Failure
10. ASA Failure - links with the parallel postulate
11. Parallel Lines - and angles associated with a transversal.
12. Triangle Angle Sum is 180 degrees - from the parallel postulate
13. Angles in Circles Easy Consequences of Properties of Isosceles Triangle
14. Drawing Circles through the vertices of Triangles with right bisectors
15. Similarity and Minimal Conditions for
16. Trig Ratios for Similar Right Triangles
17. Parallelograms and their Properties
18. Kite Construction from triangles - Reflection Across a side
19. Parallelogram Construction from triangles - Half-revolution about the center of a side.

See annotated guide below for the above steps in geometry.

Arithmetic - Ages 10+
1. Deciml Place Value - fun
2. Decimals for Tutors
3. Prime Factors - quickly
4. Fractions + Ratios
5. Arith with units - science