You could use a tabular and carefully placed \cline borders to make the lines:
\documentclass{article}
\usepackage{array}
\begin{document}
\clearpage
\begin{center}
\vspace*{1cm}
This blah blah is accepted by \\ blah blah \\ requirements for blah blah \\
\vspace{2cm}
\begin{tabular}{ c w{c}{3cm} w{c}{2.3cm} w{c}{5cm} }
Date & & & \\
\cline{2-2} \cline{4-4}
& & & blah blah, Advisor \\[2cm]
Date & & & \\
\cline{2-2} \cline{4-4}
& & & blah blah, Reader \\[2cm]
Date & & & \\
\cline{2-2} \cline{4-4}
& & & blah blah, Supervisor \\[2cm]
\multicolumn{4}{ c }{ Approved by blah blah:}
\\[2cm]
Date & & & \\
\cline{2-2} \cline{4-4}
& & & blah blah, Approver \\[2cm]
\end{tabular}
\end{center}
\end{document}