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\begin{document}

\noindent
{\Large 
Geometry Worksheet I  \hfill Name:\underline{\hspace{2.8in}}\\ \\
MA~202 \\
Spring Semester 2004}
\vspace{.25in}

\noindent
{\bf WARNING:}  You must {\bf SHOW ALL OF YOUR WORK}.  You will receive 
NO CREDIT if you do not show your work.

\noindent
{\bf DUE:} {\bf ????} 
\begin{enumerate} 
\item What are vertical angles?  Explain why vertical angles have the same
measure.
\item What are corresponding angles?  Include a general picture with your
answer.
\item What are alternate interior angles?  Prove the Alternate Interior
angles Theorem.  
\item Explain how you would convince a student that the sum of the measures
of the angles in a triangle is $180^{\rm o}$.
\item Prove that the sum of the measures of the angles of a triangle is
$180^{\rm o}$.
\item Use what you know about the angles of a triangle to find the sum 
	of the measures of the interior angles of the following figures.
	\begin{enumerate}
	\item 
		Do this problem two different ways. \\
		\epsfbox{pictures/hexagon.eps}  
	\item \mbox{\input{pictures/concavepentagon.tex}}
	\item \mbox{\input{pictures/concavepolygon.tex}}
	\end{enumerate}
\item Based on your observations from the previous question, make a
conjecture about the sum of the interior angles of an $n$-gon.  How would
you use triangles to justify your formula?
\item What is the measure of each interior angle of a regular $n$-gon?
Justify your answer.
\item What is the measure of each exterior angle of a regular $n$-gon?
Justify your answer.
\item What is the measure of each central angle of a regular $n$-gon?
Justify your answer.
\item Draw polygons of the following types, if possible.  If it is not
possible to draw such a polygon, explain why it is not possible.
	\begin{enumerate}
	\item A polygon which is equilateral but not equiangular.
	\item A polygon which is equiangular but not equilateral.
	\item A triangle which is equilateral but not equiangular.
	\item A triangle which is equiangular but not equilateral.
	\end{enumerate}
\item Circle the correct answer.
	\begin{enumerate}
	\item Counterclockwise angles have (positive, negative) measure.
	\item Clockwise angles have (positive, negative) measure.
	\end{enumerate}
\item Do numbers 4a, 5, and 12--19 in section 11.1 of your textbook.
\item Do numbers 1--4, 7--8, 11--13, and 16--19 in section 11.2 of your
textbook.
\end{enumerate}
\end{document}
