Lab Assignments

\begin{document} \maketitle 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 your lab report. Submit the 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} \section{Comments} You may discuss any and all difficulties you have with any part of this assignment on the Moodle Forum. \end{document}