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\begin{document}
\begin{center}
\Huge{\hspace{-1.5in}tcore 122: Midterm}
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\normalsize





\noindent  
\begin{enumerate}

\item $[8]$ (Quiz 1 \#2)Consider the diagram on the right.  \\
 Find: 
\begin{enumerate}
\item the measure of $\angle BCH$
\vskip .4in
\item a pair of corresponding angles\\
where we treat $\overrightarrow{AD}$ as a \\
transversal of $F$ and $G$
\vskip .4in
\item the measure of $\angle HCE$
\vskip .4in
\item the measure of $\angle ACF$.
\vskip .4in
\item a pair of similar triangles
\vskip .4in
\item whether $F$ is parallel $G$ or not.  \emph{Justify} your answer. \\(Hint: Consider using some of your work from above.)
\end{enumerate}

\vspace{-6in}\hspace{1.7in}\includegraphics[height=6.5in]{Quiz1b}	



\item Consider the tools, physical tools, for a moment....
\begin{enumerate}
\item $[2]$ (Lecture 3/28) What tools are you allowed to use during patty paper worksheet investigations?
\vskip .5in
\item $[2]$ (Lecture 4/11) Name two tools mathematicians born before 100AD could use to study geometry problems?
\vskip .5in
\item $[2]$ (Lecture 4/11) Name two tools mathematicians born before 100AD could \emph{not} use to study geometry problems?
\vskip .5in
\end{enumerate}




\newpage
\item $[2]$ (Wheater \S1.3) Make a conditional statement that is false, but whose converse is true.
\vskip 1in

\item $[4]$ (Quiz 2 \#3) The two lines $l$ and $m$ are parallel.  Find the measure of angle $x$.  Make sure that your \emph{reasoning} is easy to follow.  Note, this diagram is not drawn to scale. 

\vspace{-1.5in}\hspace{2.5in}\includegraphics[height=5in]{Midtermd}  

\item $[4]$ (Wheater \S7.4 \#18) If $\triangle VWX \sim \triangle LIP$, $VW=2x+6$, $VX=6$, $LP=7$, $LI=3x-5$, find the measure of $LI$

\vfill	



\newpage
\item $[4]$ (Lecture 4/20) Identify the base each of the origami directions below make use of.
	


\hspace{-.7in}\includegraphics[height=4in, angle=-90]{OrigamiTurtle}  

\vspace{-3.3in}\hspace{3.5in}\includegraphics[height=4in]{OrigamiCrane} 



\item $[3]$(Lang) Identify what the origami symbols below mean.

\vspace{-.7in}\begin{center}
\includegraphics[height=2.5in]{Midterma}\includegraphics[height=2.5in]{Midtermb}\includegraphics[height=2.5in]{Midtermc}
\end{center}	


\vspace{-.3in}\item $[3]$ (Quiz 3 \#5) Justify the following quote found on page 46 of Lang's text:

\hspace{1in} \emph{Generally, the more long points a model has, the smaller}\\

\vspace{-.2in}\hspace{1in} \emph{the final model will be relative to the size of the square.}

\vspace{1.5in}
\newpage
\item Okasha spends chapter 1 of his book \emph{Philosophy of Science, a Very Short Introduction} trying to define science.  
\begin{enumerate}
\item $[1]$ What did Okasha decide the definition of science should be?
\vskip 1in
\item $[1]$ How would you define a scientist?
\vskip 1in
\end{enumerate}



\item (Technical Communication Today) Richard Johnson-Sheehan gave a long list of suggestions to authors of instruction sets.  \begin{enumerate}
\item $[1]$ Identify one of his suggestions that you use well.
\vfill
\item $[1]$ Identify one of his suggestions that you think \emph{if you used this suggestion}, it  would improve your write-ups for the worksheets.
\vfill
\end{enumerate}

\item $[2]$ (Lecture 4/20) What was the most surprising/interesting information you learned from the video \emph{Between the Folds} shown on 4/20?
\vfill

\newpage
\item $[10]$ Consider a patty paper square where each side has length one.  The area of this square is then one square unit.  Find a  \emph{square} inside the patty paper that has half the area of the original patty paper. Explain your process and \emph{justify} why your method works.  

Hint: the area of a square is base $\cdot$ height or $(\text{base})^2$.

This is a patty paper exercise so the only tools you may use are patty paper(s), a pencil, and a calculator.  


\end{enumerate}

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