Lab Assignments
5sep14

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The purpose of this lab assignment is to help you become proficient
computer based geometry construction programs, and with the LaTeX
mathematical typesetting language we use. As such, this lesson
fits into the fifths theme of the course, how computers influence
geometry instruction.

Solve each of the 3 construction problems posed below. We will start on
them in lab, but you will finish them at home on your own computer. You
may use either GEX2.0, as documented in Advice, or GeoGebra.

\section{Instruction}
When announced, submit a single .pdf document in LaTeX treating each
of these constructions in separate sections of the document.
Include captioned figures made from annotated prints of constructions
you made. As with all homework, you submit a paper copy of the .pdf
you put on the Moodle.

There is also a place on the Moodle where you deposit at least one
working file for GeoGeBra (suffix .ggb) and/or GEX2.0 (suffix .gex)
much sooner (starting M3) to let me check that you are doing things
the right way. The files should be labelled something like this
(if your netid were "ivanho7", which it isn't, of course.)

F2ivanho7construction1.ggb ( or 2,3, ... or ending in .gex etc)

There is a second place in the Moodle where you can submit drafts of
LaTeX code file (suffix .tex) on the Moodle. It is also called the
"workspace" on texWins.  Be sure to also submit any figures so I can
compile your .tex file to a draft .pdf file for comments. Submit the
file(s) labelled as

M5ivanho7draft.tex  and  M5ivanho7report.pdf

\section{Experiments}
\begin{itemize}
\item Construction 1: Connect the midpoints of a given triangle. This
new triangle is called the \textit{mid-triangle} of the original one.
Then construct the centroid of both triangles. What theorem have you
discovered? Try to prove your conjecture rigorously using the methods
in the course.
\item Construction 2: Given a triangle, construct a new triangle
whose mid-triangle is the given one. This "reverses" the process
in construcion 1. How many solutions to this problem are there?
Try to prove this rigorously.
\item Construction 3: Draw a quadrilateral and its diagonals. There
are three quadrilaterals you can trace in this figure. Connect consecutive
midpoints of each of the three quadrilaterals. Use colors. Wiggle the figure
to visualize the animated image. What does it look like to you?
\end{itemize}
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