Side-Side-Side Triangle Method for
Triangle Construction and Duplication
Given the length of three side of a triangle ABC, we can
construct an isometric triangles DEF and DFH with the use of a
straight lines, or ruler and compass. The construction method
is described in greater detail below. Click on image
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SSS method
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Given the length of 3 sides of an existing triangle, we can
use ruler and compass (or strings) to construct an
isometric copy or two.
Method.
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Step 1. Draw a base DF equal in
length to the larges side AC of the original
triangle.
Step 2. Draw circles with radii
given by the lengths of the other two sides in
triangle ABC, centred at end-points D and F of
line segment DF.
Step 3. use the intersection points
of the circles, here labeled E and F to provide a
third vertex of two triangles with side EF.
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Then the two resulting triangles are isometric to the
original triangle
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Empirical Remark 1: Drawings with the larger radius
circle centered at D instead of F would result in two more
triangles isometric to triangle ABC. Thus for any line
segment DF, there are upto four instances of the SSS
triangle construction method.
Empirical Remark 2: The foregoing
construction method can be applied starting with side AC
of the triangle ABC. That construction method with it
four variations would result in 4 triangles isometric to
ABC. The first would be coincident with ABC.
A second would have a vertex B' on the same side of AC as
B. A third would have a vertex D given by the
reflection of B across side AC, or the line through it.
The fourth would have a vertex D' equal to the reflection
of B' across side AC or the line through it. The
triangle AD'C would be given by a 180 degree rotation of
the triangle ABC about the center of side AC.
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SSS Isometry Assumption
If there is a correspondence between the vertices such that
corresponding sides are have equal lengths then the triangles are
isometric. Moreover, both could be built or rebuilt by the
same construction SSS method, and each may be moved by a
sequence of translations, rotations and/or reflections, so
that sides and vertices coincide with the other.
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A side-side-side like Construction - Location of a point.
Scenario 1: A point P is to be placed 20 meters away from a
point A and 25 meters away from a point B, and north of both
points. Two surveyors attach a string (or tape measures) of
length 20 meters at A and another of length 25 meters at B. Holding the
strings taught they move the other ends of the string until the ends
meet. That locates the point P.
Scenario 2. Two surveyors observe a point P is 20 meters
away from a point A, and 25 meters away from a point B, and further north
than both. On a map drawn to a scale of 1 cm to 10 meter, they
locate P on the map by finding the Northern most intersection of a circle
of radius 2.0 cm centered at the map location of A with another circle of
radius 2.5 cm centered at the map location of B. That yields the
coordinates of P on the map and actual.
Uniqueness Observation and Assumption: If one side AB of a
triangle ABC is given then the Side Side Side construction method applied
to end points of the line segment AC leads to two isometric triangles,
the original triangle ABC and a second triangle ADC - isometric by the
assumption above.
The discussion of this situation will be continued below.
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Teachers & Tutors: Site pages offer better or best practices for providing skills -
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Others are welcome to refine or exceed it. Please do.
Secondary
Mathematics for Ages 11+, A Practical Approach for home-tutoring or -schooling, or for schools & colleges
with local curriculum control. Study how to include site content - its skill development how-TOs and innovations
into present or future lesson plans - some reading required.
Road
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See too, the BBC-Belgium story Texting and
Driving - texting & the impossible test - the article links to a gruesome utube video on the subject
The Logic of Injustice:
How Texas sent
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May 2012, Composition Starting:
Pre-School and Primary Mathematics - Quantitative Skills, An
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Parent Center: Help your child or teen
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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
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McCainian: drill, drill, drill then Toronto
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Mathematics
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Skills with take
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Is your child able to add, subtract and multiply amounts
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Arithmetic
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Algebra
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Calculus Starter Lessons
Calculus Lessons Elsewhere:
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How to Ace Calculus: Street Wise Guide - Mostly
Text.
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Flash
Video for Calculus Phobics
They cover basic topics in ways likely to complement your
notes, your textbooks and site material. When Goldilocks
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Unsolicited Advice
Learning to do and high marks if it comes to easy is often
deceptive - light rather than deep. For that reason, students
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calculus and more generally in the first year of college. Bon
Appetite.
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