\documentclass[12pt]{article}
\usepackage{fullpage,amsmath,amsfonts,graphicx}

\begin{document}

\title{General Mathematics and CPS II}
\author{Exercise 6}
\date{February 22, 2012}
\maketitle

\begin{enumerate}

\item (Ivanov, p.\ 34, Problem 9.)  Consider two squares situated in
the same plane.  Join any corner of one square to any corner of the
other by means of a line segment, and then, proceeding in the same
direction around both squares, the next corner to the next, and so on.

Prove that the midpoints of the four line segments so constructed are
also the vertices of a square.


\item (Ivanov, p.\ 36, Problem~14.)  Show that
  \begin{enumerate}
  \item $R_{\ell_1} \, R_{\ell_2} = R_{\ell_2} \, R_{\ell_1}$ if and
  only if $\ell_1$ and $\ell_2$ are perpendicular;
  \item  $R_{\ell} \, H_A = H_A \, R_{\ell}$ if and
  only if $A \in \ell$.
  \end{enumerate}

\end{enumerate}
\end{document}
