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\begin{document}

\title{Geometriler al\i\c st\i rmalar\i}
\author{David Pierce}
\date{21 Aral\i k 2015}
\publishers{Matematik B\"ol\"um\"u\\
Mimar Sinan G\"uzel Sanatlar \"Universitesi\\
\.Istanbul\\
\url{mat.msgsu.edu.tr/~dpierce/}\\
\url{dpierce@msgsu.edu.tr}}
%\begin{abstract}
\maketitle

\begin{problem}
$ACE$ ve $BDF$ do\u gru ve birbirine paralel olsun.
  \begin{equation*}
    AB\parallel DE\And BC\parallel EF\implies CD\parallel AF
  \end{equation*}
gerektirmesini kan\i tlay\i n.
\end{problem}

\begin{problem}
$ABCD$ ve $EFGH$ do\u gru ise  
\begin{equation*}%\label{eqn:ACBD}
  \frac{AC\cdot BD}{AD\cdot BC}=\frac{EG\cdot FH}{EH\cdot FG}
\iff
  \frac{AB\cdot CD}{AD\cdot BC}=\frac{EF\cdot GH}{EH\cdot FG}
\end{equation*}
denkli\u gini kan\i tlay\i n.
\end{problem}
\pagebreak
\begin{problem}
\Sekilde{fig:VIII}ki durumlarda
\begin{figure}
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\uput[d](2,2){\gr A}
\uput[dl](0,0){\gr B}
\uput[dr](4,0){\gr G}
\uput[160](1,1){\gr D}
\uput{2pt}[ur](3,1){\gr E}
\uput[ul](0,4){\gr Z}
\uput[ur](3,3){\gr H}
\end{pspicture}
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\uput[dl](0,0){\gr B}
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%\uput[u](0,5){\gr H}
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\caption{Lemma VIII}\label{fig:VIII}
\end{figure}
\gr{BDH} ve \gr{GEZ} do\u grular\i\ \gr A noktas\i nda kesi\c sirse
\begin{equation*}
  \grm{BG}\parallel\grm{DE}\And\grm{BZ}\parallel\grm{EH}
\implies\grm{HG}\parallel\grm{DZ}
\end{equation*}
gerektirmesini kan\i tlay\i n.
\end{problem}

\begin{problem}\label{Q}
\Sekilde{fig:Q}
    \begin{figure}
\centering
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\begin{pspicture}(4,-0.5)(10,4.5)
\psline(4,0)(10,0)
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(4,3)(10,0)
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\uput[ul](4,4){$H$}
\uput[l](4,3){$K$}
\uput[ur](6,2){$L$}
\end{pspicture}
\caption{Problem \ref{Q}}\label{fig:Q}

\end{figure}
 $CEF$, $CKH$, $ELH$, ve $FLK$ do\u gru ise
    \begin{equation*}
      \frac{CF}{FE}=\frac{KC}{HK}\cdot\frac{HL}{LE}
    \end{equation*}
e\c sitli\u gini kan\i tlay\i n.
\end{problem}

\begin{problem}\label{CQT}
\Sekilde{fig:CQT}
  \begin{figure}
\centering
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(4,3)(10,0)
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\uput[ul](2,0){$B$}
\uput[ul](4,0){$C$}
\uput[ul](6,0){$D$}
\uput[ur](8,0){$E$}
\uput[r](10,0){$F$}
\uput[u](6,6){$G$}
\uput[ul](4,4){$H$}
\uput[l](4,3){$K$}
\uput[ur](6,2){$L$}
\end{pspicture}
\caption{Problem \ref{CQT}}\label{fig:CQT}

\end{figure}
$ABCDEF$, $AHG$, $BKG$, $CKH$, $DLG$, $ELH$, ve $FLK$ do\u gru ise
  \begin{equation*}
    \frac{AF\cdot BC}{AB\cdot CF}=\frac{AF\cdot DE}{AD\cdot EF}
  \end{equation*}
e\c sitli\u gini kan\i tlay\i n.
\end{problem}
\end{document} 
