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\begin{document}
\begin{center}
\Huge{Patty Paper Worksheet 4}

\Large{Haga's Theorem}
\end{center}
\noindent
\small{inspired by Kazuo Haga's ``Folding Paper and Enjoy Math: Origamics" in  \emph{Origami: Third International Meeting of Origami Science, Mathematics, and Education}.}
\vskip .2in

\normalsize
\begin{enumerate}
\item Take a patty paper and mark a \\
point $P$ at random along the top \\
edge of the paper.  
\item Fold the lower right corner to \\
the point $P$ as depicted.

\vspace{-3.5in} \hspace{2in} \includegraphics[height=6in]{HegaThm1}	
\vspace{-2.3in}
\item Notice that there are (usually) three triangles that are formed by the fold you made in step two.  Label the triangles $A$, $B$, and $C$ as done above.
\item What nice relationship must be true about triangles $A$, $B$, and $C$? Justify your conclusions.
\vskip 4in
	
\item Suppose that you took the point $P$ to be the \\
midpoint of the top edge.  Use your above \\
observation to find out what lengths $x$ and $y$ \\
must be in the figure to the right.

\vspace{-2.5in}\hspace{4in}\includegraphics[height=2.5in]{HegaThm2}	


\end{enumerate}




\end{document}
