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how to do "construction" problems?

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Jon Du Kim

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Aug 16, 2010, 7:45:12 AM8/16/10
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I recently picked up a copy of Nathan Altshiller Court's
"College Geometry".
Trying to work the exercises I realize that they are
somewhat foreign to me in what they ask so
I am not sure how to formulate the solutions.
He discusses the method of
Analysis, Construction, Proof, Discussion in doing these
problems but I am still not sure I am doing them right.
For example,
Problem:
Construct a triangle given a, B, C
My solution:
Analysis: Given the side a and the two vertex angles
B and C the corresponding sides b and c complete the
triangle
Construction: Construct sides b and c to form
triangle ABC
Proof: Follows immediately from the definition of a
triangle
Discussion: I am not sure if this is how to
formulate the solution.

Is my solution correct and is this how these things are
done? Any advice?

Thanks!

Ben Saucer

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Aug 16, 2010, 2:22:30 PM8/16/10
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Were you given a diagram? I would assume that you were given a segment
and two angles (labeled) but not connected as a triangle. A
constructions are done using a straight-edge and compass. Actually you
are to write down each step along with their "reason". In this case you
are to copy the given parts into new locations so that they form a
triangle.

Copy the segment "a" to be the same length as the given "a" (or you may
use the original "a" without copying it.) Label the end points "B" and "C".

Copy the two given angles "B" and "C" to the end points of "a". The
constructed rays of those angles are extended to meet at a new point "A".

Jon Du Kim

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Aug 16, 2010, 3:06:04 PM8/16/10
to geometry...@moderators.isc.org
No, no diagram was given...the givens were just listed.
Your description of the solution is very helpful.
I graduated HS in the US in 1992 and these sorts of
problems were never used then. I've seen recent HS
geometry texts and these are certainly not seen!
I feel bad...almost liked I missed out or something. :)
I thought that by getting the book and try a few out
it would be fun. I think it is...I just need some guidance.
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