2 Euclidean Geometry Constructions Theory extras
Short Course on Euclidean Geometry
1 Initial Concepts and Terms
2 Correspondence between Triangles
3 Isometry of Triangles - Congruence
4 Side Side Side
5 Side Angle Side
6 Ruler and compass Angle Bisection
7 Angle Side Angle
8 Isoceles Triangles
9 Construction of a right bisector
10 Dropping a perpendicular to line
11 Triangle Construction Fails
12 Side Angle Side Failure
13 Angle Side Angle Failure
14 Parallel Lines Postulate
15 Triangle Angle Sum is 180 degrees
16 Angles Subtended By Chords and Diameters
17 Right Bisectors of Triangle Sides
18 Triangle Similarity Take 1
19 Right Triangle Similarity
21 Parallelograms
PS A Kite Construction Methods
PS B Parallelogram Construction Methods
PS C Similarity Use - Recognize it in Trigonometry
PS D Addition with Cartesian Coordinates
PS E Multiplication with Polar Coordinates
PS F Scalar Multiplication Distributes over Addition
PS G Rotation Distributes over Addition
PS H Distributive Law For Complex Numbers
Euclidean Geometry Elsewhere - LINKS
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.
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In North America, primary secondary students will learn to
recognize and identify parallel lines, transversals, circles,
rectangles and like shapes. They will aso learn about coordinates.
Older secondary school students may also learn trigonometry. But
Euclidean Geometry present before the 1990s will be skipped. Course
designers decided that it is too hard. In my youth the given
Euclidean Geometry proofs of the Pythagorean Theorem, the Chinese
square dissection proof, understandable after the mastery of some
algebra, provides a simpler alternative.
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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 required for the site
development of analytic geometry and trigonometry.
-
Common Terms and
Vocubulary: Points, lines, rays, line segments.
-
Correspondence
between triangles. Here is an explicit definition, not always seen in
class.
-
Isometry of
Triangles - Here is a definition.
-
Side-Side-Side (SSs) method for
triangle construction and SSS like method for locating point.
-
Side Angle Side (SAS) method
plus an application
Ruler and
Compass Construction to Bisect an Angle
-
Angle-Side-Angle (ASA)method,
and ASA-like method for determining current location in navigation.
-
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)
-
Side-Side-Side
Failure
-
SAS Failure or Near
Failure
-
ASA Failure - links
with the parallel postulate
-
Parallel Lines - and
angles associated with a transversal.
-
Triangle Angle
Sum is 180 degrees - from the parallel postulate
-
Angles
in Circles Easy Consequences of Properties of Isosceles Triangle
-
Drawing Circles
through the vertices of Triangles with right bisectors
-
Similarity and
Minimal Conditions for
-
Trig Ratios
for Similar Right Triangles
-
Parallelograms and their
Properties
-
Kite Construction
from triangles - Reflection Across a side
-
Parallelogram
Construction from triangles - Half-revolution about the center of a
side.
Euclidean Geometry - 2nd Description of Section Content.
A different perspective - Partially Redundant.
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.
-
Common Terms and
Vocubulary: Points, lines, rays, line segments.
-
Correspondence
between triangles. Here is an explicit definition, not always seen in
class.
-
Isometry of
Triangles - Here is a definition.
-
Side-Side-Side (SSs) method for
triangle construction and SSS like method for locating point.
-
Side Angle Side (SAS) method
plus an application
Ruler and
Compass Construction to Bisect an Angle
-
Angle-Side-Angle (ASA)method,
and ASA-like method for determining current location in navigation.
-
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)
-
Side-Side-Side
Failure
-
SAS Failure or Near
Failure
-
ASA Failure - links
with the parallel postulate
-
Parallel Lines - and
angles associated with a transversal.
-
Triangle Angle
Sum is 180 degrees - from the parallel postulate
-
Angles
in Circles Easy Consequences of Properties of Isosceles Triangle
-
Drawing Circles
through the vertices of Triangles with right bisectors
-
Similarity and
Minimal Conditions for
-
Trig Ratios
for Similar Right Triangles
-
Parallelograms and their
Properties
-
Kite Construction
from triangles - Reflection Across a side
-
Parallelogram
Construction from triangles - Half-revolution about the center of a
side.
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For home-tutoring or -schooling, or for schools or colleges
with course content control: Secondary
Mathematics for Ages 11+, A Practical Approach.
May 2012, Composition Starting:
Pre-School and Primary Mathematics - Quantitative Skills, An
Intellectual View, Feedback Welcome:
The 8 Most Popular Site Inlinks
Parent Center: Help your child or teen
learn:
Parent-friendly
Work Booklets for ages 3+ to 13 Use these or others to check
or build skills. Other booklets are available but these booklets
allow parents unsure of themselves in mathematics to help their
children. The selection acquired in Canada is published in the
USA. So it has a US orientation. In retrospect, the selection
shows parents what to check with the booklets or by other ways,
the choice is theirs. But in retrospect, the selection does not
cover integral and fractions liquid weights and measures - ask
the publishers to correct that! For ages 9 to 12 say, parents may
compensate by showing boys and girls how to use weights or mass,
and further measures in food preparation. Beyond that children
may be shown how to measure and calculate angles, lengths and
areas [proportional amounts too] directly or by using maps and
plans drawns to scale. Learning how to gather and measure all the
ingredients, pots and pans for a dish or a meal, along with
cleaning up sets the stage for like activities or experiments in
science courses, and in developing organizational skills,
gives boys and girls a head start. Good luck. At the other
extreme, more comprehensive than light, if your motto is
McCainian: drill, drill, drill then Toronto
mathematician and actor John Mighton's jump math organization has jump math
workbooks for at least grades 3 to 8 for at-home and in-school
use - training sessions for teachers available. Jump math has
been expanding to cover older students. Jump Math Samples: plus
Fractions for
Grades 3-4 & Grades 5-6 [Read] Free Resources grades 1 to 8
[unread - likely to be good]. and
Mathematics
Skills For Ages 3 to 14 - technical!
Skills with take
home value - A few ideas
Basic skills include
time-date-calendar Matters; money matters; map, plan and
scale diagram matters;counting, measuring and figuring;
decision making with logic and likelyhood; being careful and
being aware of the domino effect of mistakes; reading and
writing with precision.
Is your child able to add, subtract and multiply amounts
of money, work with fractions, work with clocks and calendars,
work with maps and plans, and measure length, weight-mass and
volume? Schools may promote your son or daughter without
providing basic skills in reading, writing and
arithmetic.
Arithmetic
and Number Theory Skills
Algebra
Starter Lessons
Geometry
- maps plans trigonometry vectors
More
Algebra
70
Calculus Starter Lessons
Calculus Lessons Elsewhere:
-
How to Ace Calculus: Street Wise Guide - Mostly
Text.
-
Flash
Video for Calculus Phobics
They cover basic topics in ways likely to complement your
notes, your textbooks and site material. When Goldilocks
trespassed in the house of the three bears, she found three bowls
of porridge, two not to her liking, and one just right. Different
bears have different tastes. As invited guest here and elsewhere,
if one or more explanations is not to liking, try another. It may
be better or just right.
Unsolicited Advice
Learning to do and high marks if it comes to easy is often
deceptive - light rather than deep. For that reason, students
with learning difficulties determined not to let it get in their
way may go deeper and farther than those with none. High marks,
if the come easy, may be deceptive - provide a too light and not
a deep mastery. That could have been your problem in secondary
school, one that leads to comprehension shock or difficulties in
calculus and more generally in the first year of college. Bon
Appetite.
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