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\theoremstyle{definition}
\newtheorem{soru}{Soru}
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\begin{document}

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\mbox{}

\mbox{}

\noindent\begin{picture}(0,0)
  \put(0,60){\sf Ad - Soyad:}
  \put(0,30){\sf Öğrenci Numarası:}
\end{picture}%
{\Large MSGSÜ, MAT 113, Sınav}\hspace{\stretch{1}} 
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\raisebox{-3cm}[0cm][0cm]{\begin{tabular}[b]{|c|p{1cm}|}\hline 
       1&\\
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\hline $\Sigma$&\\ \hline
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5 Kasım 2012, Saat 15:00

\vspace{1ex}

\parbox{12cm}{\textbf{Öğretmenler:} Ahmet Bakkalo\u glu, Ayhan G\"unayd\i n,\\
\mbox{}\hfill Özer Öztürk, David Pierce}

\vspace{1ex}

\parbox{12cm}{%\textbf{Yönergeler}: 
\textbf{A\c c\i klamalar:}
Sınavda 4 sayfada 5 soru var.
%Notlandıran için çözümlerinizin nasıl okunacağı açık olmalı. 
Lütfen
dikkat ederek yazın.
\"Oklid'in
ilk 20 \"onermesini kullanabilirsiniz.
} 

\begin{soru}
Fig\"urde
\begin{compactitem}
\item 
$CBD$, merkezi $A$ olan bir \c cember;
\item 
$CAD$, merkezi $B$ olan bir \c cember;
\item
$AEB$ ile $CED$, do\u gru \c cizgiler
\end{compactitem}
olsun.  $AEC$ a\c c\i s\i n\i n dik a\c c\i\ oldu\u gunu g\"osterin.
\hfill
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\uput[l](1,1){$A$}
\uput[r](2,1){$B$}
\uput[u](1.5,1.82){$C$}
\uput[d](1.5,0.18){$D$}
\uput[ur](1.5,1){$E$}
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\hfill\mbox{}
\end{soru}

\begin{cozum}\mbox{}
\begin{compactenum}
\item
$AC=AB$ [\c cemberin yar\i\c caplar\i]
\item
$CB=AB$ [ayn\i]
\item
$AC=CB$ [1.\ genel kavram]
\item
$AD=DB$ [benzer]
\item
$CD$ kenar\i, $ACD$ ve $BCD$ \"u\c cgenlerinin ortak kenar\i d\i r.
\item
$ACD=BCD$ [8.\ \"onerme]
\item
$CE$ kenar\i, $ACE$ ve $BCE$ \"u\c cgenlerinin ortak kenar\i d\i r.
\item
$AEC=BEC$ [4.\ \"onerme]
\end{compactenum}
\end{cozum}

\newpage

\begin{soru}
Fig\"urde
\begin{compactitem}
\item
$AB=DE$, $BC=EF$, $AC=DF$, $BG=EH$, $AG=KH$;
\item
$BGA$ ile $EHK$ a\c c\i lar\i, dik
\end{compactitem}
olsun.  Fig\"ur\"un imk\^ans\i z oldu\u gunu g\"osterin, yani $K$ ile
$D$ noktalar\i n\i n farkl\i\ noktalar olamad\i\u g\i
n\i\ g\"osterin. 
\begin{center}
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\uput[u](2,2){$A$}
\uput[d](0,0){$B$}
\uput[d](3,0){$C$}
\uput[d](2,0){$G$}
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\qquad\qquad
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\end{soru}

\begin{cozum}\mbox{}
\begin{compactenum}
\item
$AGB=KHE$ [4.\ post\"ulat]
\item
$KE=AB$ [4.\ \"onerme]
\item
$AGC$ ile $KHF$, dik a\c c\i lar [13.\ \"onerme]
\item
$AGC=KHF$ [4.\ post\"ulat]
\item
$GC=HF$ [3.\ genel kavram]
\item
$AC=KF$ [4.\ \"onerme]
\item
$KE=DE$ ve $KF=DF$ [1.\ genel kavram]
\item
$K$ ile $D$, farkl\i\ olamaz [7.\ \"onerme]
\end{compactenum}
\end{cozum}


\newpage

\begin{soru}
\mbox{}
\begin{compactitem}
\item
A\c c\i lar\i n\i n biri dik olan,
\item
en k\i sa kenar\i\ verilmi\c s do\u gru olan,
\item
o kenar\i\ g\"oren a\c c\i s\i\ kalan dik olmayan a\c c\i s\i n\i n yar\i s\i\ olan
\end{compactitem}
bir \"u\c cgen in\c sa edin.  (Yani en k\i sa kenar\i\ verilmi\c s bir
do\u gru olan bir `30-60-90' \"u\c cgen in\c sa edin.)  
\end{soru}

\begin{cozum}
\mbox{}
\begin{compactenum}
\item
Verilmi\c s do\u gru $AB$ olsun
\item
Bu do\u gru, $C$ noktas\i na uzat\i ls\i n [2. post\"ulat]
\item
$BC=AB$ olsun [3.\ \"onerme]
\item
$AC$ do\u grusunda $ACD$ e\c skenar \"u\c cgen in\c sa edilsin.  [1.\ \"onerme]
\item
$DB$ birle\c stirilsin [1. post\"ulat]
\item
$ADB=BDC$ [8.\ \"onerme]
\item
$DAB=ADC$ [5.\ \"onerme]
\item
$ADB$, $DAB$ a\c c\i s\i n\i n yar\i s\i
\item
$ADB$ \"u\c cgeni, istenen \"u\c cgendir
\end{compactenum}
\end{cozum}

\newpage

\begin{soru}
Aşağıdaki önermede hangi ad\i m, \"Oklid'in ilk 4 post\"ulat\i\ ve ilk
20 \"onermesi kullan\i larak do\u grulanamaz. 
\begin{compactenum}
\item
T\"um e\c skenar \"u\c cgenlerin t\"um a\c c\i lar\i n\i n birbirine
e\c sit oldu\u gunu g\"osterece\u giz. 
\item
$ABC$ ile $DEF$, e\c skenar \"u\c cgenler olsun.
\item
$A$ a\c c\i s\i n\i n $D$ a\c c\i s\i na e\c sit oldu\u gunu g\"osterece\u giz.
\item
$AB=DE$ ise, $BC=DF$ ve $AC=DF$ de olur.
\item
O halde $A$ a\c c\i s\i\ $D$ a\c c\i s\i na e\c sit olmal\i.
\item
$AB<DE$ olsun.
\item
O zaman $AC<DF$.
\item
$DE$ kenar\i ndan $AB$ kenar\i na e\c sit olan $DG$ do\u grusu kesilsin.
\item
$DF$ kenar\i ndan $AC$ kenar\i na e\c sit olan $DH$ do\u grusu kesilsin.
\item
$G$ ile $H$ noktalar\i\ birle\c stirilsin.
\item\label{hatali}
O zaman $DGH$ \"u\c cgeni, eskenar \"u\c cgendir.
\item
$GH=BC$.
\item
$A$ a\c c\i s\i, $D$ a\c c\i s\i na e\c sittir.
\item
$DE<AC$ ise, benzer \c sekilde $A$ a\c c\i s\i, $D$ a\c c\i s\i na e\c
  sittir.
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\end{compactenum}
\end{soru}

\begin{cozum}
\ref{hatali}.\ ad\i m hatal\i d\i r.
\end{cozum}

\vfill

\begin{soru}
A\c sa\u g\i daki sorular\i n \emph{biriyi} \c c\"oz\"un.
\begin{enumerate}[A.]
\item
Aşağıdaki bitkilerin ve deniz hayvanlar\i n\i n isimleri Türkçede nedir?
\begin{center}
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\makebox[0pt][c]{
\begin{tabular}{|c|c|c|c|c|c|c|}\hline
\gr{AGKINARA} & \gr{ASTAKOS} & \gr{KASTANIA} & \gr{MUDIA} & \gr{PRASO} & \gr{STREIDIA} \\
\hline
 & & & & &\\\hline
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\item
  Yunan alfabesini s\i ras\i nda yaz\i n:
  \begin{center}
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    \begin{tabular}{*{24}{|c}|}\hline
\phantom{\rule{2.4mm}{7mm}}
&
\letter&
\letter&
\letter&
\letter&
\letter&
\letter&
\letter&
\letter&
\letter&
\letter&
\letter&%\\\hline\hline
\letter&
\letter&
\letter&
\letter&
\letter&
\letter&
\letter&
\letter&
\letter&
\letter&
\letter&
\letter\\\hline
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  \item
  \"Oklid'in ilk 6 \"onermesi i\c cin, kulland\i\u g\i\ \"onermeleri (ve sadece onlar\i) yaz\i n:
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  \begin{tabular}{|c|c|}
  \hline
  1&\phantom{\rule{4cm}{7mm}}\\\hline
  2&\\\hline
  3&\\\hline
  4&\\\hline
  5&\\\hline
  6&\\\hline
  \end{tabular}
  \end{center}
\end{enumerate}
\end{soru}

\end{document}
