\documentclass{beamer}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% Fichier de style de T. Duvoid -- version du 14/11/2007%
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\usetheme{progressbar}
%Les extensions utilis\'ees

\usepackage{pstricks}
\usepackage{pst-plot,pstricks-add,pst-math,pst-xkey,pst-eucl,pst-tree,pst-node} %manque picins

\usepackage[utf8]{inputenc}



%Cr\'eation des ensembles math\'ematiques
\newcommand{\N}{\ensuremath{\mbox{I\hspace{-.15em}N}}\xspace}
\newcommand{\R}{\ensuremath{\mbox{I\hspace{-.15em}R}}\xspace}
\newcommand{\C}{\ensuremath{\mbox{l\hspace{-.47em}C}}\xspace}
\newcommand{\Z}{\ensuremath{\mbox{Z\hspace{-.3em}Z}}\xspace}
\newcommand{\Q}{\ensuremath{\mbox{l\hspace{-.47em}Q}}\xspace}
\newcommand{\D}{\ensuremath{\mbox{I\hspace{-.15em}D}}\xspace}

%Arc de cercle 
 \newlength{\longarc} 
 \newcommand{\arc}[1]{\settowidth{\longarc}{$#1$}% 
         \addtolength{\longarc}{-0.5em}% 
 \unitlength \longarc% 
 \ensuremath{% 
         \stackrel{\begin{picture}(1,0.2) 
                 \qbezier(0,0)(0.5,0.2)(1,0) 
         \end{picture}} 
         {#1} 
 }}
%flèches d'\'equivalence et de vecteurs
\newcommand{\ssi}{\ensuremath{\Longleftrightarrow}}
\newcommand{\vecteur}[1]{\overrightarrow{#1\;}}


%
%%%%%%%%%%%
%Symbole Attention
\font\manual=manfnt
\newcommand{\danger}{{\manual\symbol{127}}}
%%%%%%%%Pour des flËches dans les tableaux de variation
\newcommand{\cro}{% croissante
\unitlength=1cm
\begin{minipage} {1cm}%pour centrer verticalement f(x)
  \begin{picture}(1,1)    % dessin de 2 X 2
     \put(0,0){\vector(1,1){1}} % 1 ‡ partir (0,0) direction (1,1)  
 \end{picture} 
\end{minipage}
}
\newcommand{\dec}{%dÈcroissante
\unitlength=1cm
\begin{minipage} {1cm}%pour centrer verticalement f(x)
  \begin{picture}(1,1)    % dessin de 2 X 2
     \put(0,1){\vector(1,-1){1}} 
 \end{picture} 
\end{minipage}
}
%%toutes les maths en style math
\everymath{\displaystyle}
%%
\newcommand{\repere}{$(O;\vec{\imath},\vec{\jmath})$}
%%
\newcounter{numex} 
\def\Ex#1{\addtocounter{numex}{1} \mbox{\large{\textsc{Exercice}} 
\thenumex { \scriptsize #1}}}

%\def \points#1%
%{%
%\if -#1
%\xspace%
% \else
%{\small ( #1 points )}\xspace%
%\fi
%}
%pour compatibilitÈ ancienne version
\def\exop#1{\exo[#1]}
%%%%%%%%%%%%%%%%%%%%%%%%%%
\DeclareMathOperator{\e}{e}




\title{\textsc{\large{~}}}
\author{Aude Duvoid}
\begin{document}

\begin{frame}
	\frametitle{Calcul de longueurs}\\ 
	Sur la figure ci-dessous, $A \in [GL]$, $E \in [GK]$, $(AE) \sslash (LK) $, $AG=5,4$ cm, $GE=3$ cm, $GK=5$ cm et $LK=11$ cm.\\
	Calculer les longueurs $GL$ et $AE$.
	\begin{center}
		\psset{xunit=1.0cm,yunit=1.0cm,algebraic=true,dotstyle=o,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
		\begin{pspicture*}(-3,-0.6)(4,4.4)
		\psline(-2.16,-0.32)(1.4,4)
		\psline(1.4,4)(3.14,0.9)
		\psline(3.14,0.9)(-2.16,-0.32)
		\psline(-0.74,1.4)(2.45,2.13)
		\rput[bl](-2.44,-0.34){$L$}
		\rput[bl](1.48,4.12){$G$}
		\rput[bl](3.22,1.02){$K$}
		\rput[bl](-1.04,1.52){$A$}
		\rput[bl](2.52,2.26){$E$}
		\end{pspicture*}
	\end{center}
\end{frame}


\begin{frame}
	\frametitle{\textsc{Théorème de Thalès}}
		\begin{minipage}{3cm}
			\begin{center}
				\psset{xunit=0.4cm,yunit=0.4cm,algebraic=true,dotstyle=*,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
				\begin{pspicture*}(-1.3,-1.1)(4.48,5.3)
				\psplot{-1.3}{4.48}{(-1.85-3.8*x)/0.12}
				\psplot{-1.3}{4.48}{(--12.59-2.7*x)/3.38}
				\psplot{-1.3}{4.48}{(--1.92--1.1*x)/3.26}
				\psplot{-1.3}{4.48}{(--7.25--1.1*x)/3.26}
				\rput[bl](-0.54,4.34){$A$}
				\rput[bl](-0.42,0.7){$B$}
				\rput[bl](2.7,1.7){$C$}
				\rput[bl](-0.48,2.3){$M$}
				\rput[bl](1.4,3){$N$}
				\end{pspicture*}
			\end{center}
		\end{minipage}
		\begin{minipage}{3cm}
			\begin{center}
				\psset{xunit=0.4cm,yunit=0.4cm,algebraic=true,dotstyle=*,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
				\begin{pspicture*}(-1.3,0.2)(3.2,5.2)
				\psplot{-1.3}{3.2}{(-0.2-1.82*x)/0.22}
				\psplot{-1.3}{3.2}{(--7.83-1.12*x)/2.02}
				\psplot{-1.3}{3.2}{(--4.6--0.7*x)/1.8}
				\psplot{-1.3}{3.2}{(--2.62--0.7*x)/1.8}
				\rput[bl](-0.54,4.34){$A$}
				\rput[bl](-1.32,2.52){$B$}
				\rput[bl](1.3,3.3){$C$}
				\rput[bl](-0.2,0.5){$M$}
				\rput[bl](2,1.3){$N$}
				\end{pspicture*}
			\end{center}
		\end{minipage}
		\begin{minipage}{3cm}
			\begin{center}
				\psset{xunit=0.4cm,yunit=0.4cm,algebraic=true,dotstyle=*,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
				\begin{pspicture*}(-2.5,1.5)(2.5,7)
				\psplot{-2.5}{2.5}{(-0.2-1.82*x)/0.22}
				\psplot{-2.5}{2.5}{(--7.83-1.12*x)/2.02}
				\psplot{-2.5}{2.5}{(--4.6--0.7*x)/1.8}
				\psplot{-2.5}{2.5}{(--10.16--0.7*x)/1.8}
				\rput[bl](-0.54,4.34){$A$}
				\rput[bl](-0.32,1.52){$B$}
				\rput[bl](1.2,3.22){$C$}
				\rput[bl](-0.68,5.7){$M$}		
				\rput[bl](-1.9,5.2){$N$}
				\end{pspicture*}
			\end{center}
		\end{minipage}

\begin{alertblock}{~}
	\begin{minipage}{1cm}
	\textsc{Si}
	\end{minipage}
	\begin{minipage}{3cm}
		\begin{itemize}
			\item $M$ est un point de la droite $(AB)$,
			\item $N$ est un point de la droite $(AC)$,
			\item les droites $(BC)$ et $(MN)$ sont parallèles,
		\end{itemize}
	\end{minipage}
	\begin{minipage}{1.5cm}
	\textsc{Alors}
	\end{minipage}
	\begin{minipage}{4cm}
		 $\frac{AM}{AB}=\frac{AN}{AC}=\frac{MN}{BC}$
		\end{minipage}
\end{alertblock}	
\end{frame}


\begin{frame}
	\begin{minipage}{6cm}
		Les droites $(BC)$ et $(MN)$ sont parallèles.\\
		$AB=3$ cm ; $AN=4$cm et \\ $AM=7$cm.\\ \\
		Calculer la longueur $AC$.
	\end{minipage}
	\begin{minipage}{4cm}
		\begin{center}
			\psset{xunit=0.5cm,yunit=0.5cm,algebraic=true,dotstyle=*,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
			\begin{pspicture*}(-1.3,-1.1)(4.48,5.3)
			\psplot{-1.3}{4.48}{(-1.85-3.8*x)/0.12}
			\psplot{-1.3}{4.48}{(--12.59-2.7*x)/3.38}
			\psplot{-1.3}{4.48}{(--1.92--1.1*x)/3.26}
			\psplot{-1.3}{4.48}{(--7.25--1.1*x)/3.26}
			\psdots(-0.62,4.22)
			\rput[bl](-0.54,4.34){$A$}
			\psdots(-0.5,0.42)
			\rput[bl](-0.42,0.54){$B$}
			\psdots(2.76,1.52)
			\rput[bl](2.84,1.64){$C$}
			\psdots(-0.55,2.04)
			\rput[bl](-0.48,2.16){$M$}
			\psdots(1.32,2.67)
			\rput[bl](1.4,2.8){$N$}
			\end{pspicture*}
		\end{center}
	\end{minipage}	
\end{frame}

\begin{frame}
	\begin{minipage}{6cm} Les droites $(CD)$ et $(HT)$ sont parallèles.\\
		$DG=25$ mm ; $GH=45$ mm ; $CG=20$ mm et $HT==27$ mm.\\
		Calculer $GT$ et $CD$.
	\end{minipage}
	\begin{minipage}{4cm}
		\begin{center}
			\psset{xunit=0.5cm,yunit=0.5cm,algebraic=true,dotstyle=*,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
			\begin{pspicture*}(-2.5,1.5)(2.5,7)
			\psplot{-2.5}{2.5}{(-0.2-1.82*x)/0.22}
			\psplot{-2.5}{2.5}{(--7.83-1.12*x)/2.02}
			\psplot{-2.5}{2.5}{(--4.6--0.7*x)/1.8}
			\psplot{-2.5}{2.5}{(--10.16--0.7*x)/1.8}
			\psdots(-0.62,4.22)
			\rput[bl](-0.54,4.34){$G$}
			\psdots(-0.4,2.4)
			\rput[bl](-0.32,2.6){$H$}
			\psdots(1.4,3.1)
			\rput[bl](1.48,3.3){$T$}
			\psdots(-0.76,5.35)
			\rput[bl](-0.68,5.6){$D$}
			\psdots(-1.87,4.92)
			\rput[bl](-1.8,5.2){$C$}
			\end{pspicture*}
		\end{center}
	\end{minipage}
\end{frame}


\begin{frame}
	\frametitle{\textsc{Bleu}}
	$BLEU$ est un rectangle, $(EB)$ et $(RI)$ sont parallèles.\\
	Le triangle $UIR$ est-il rectangle ? Justifier la réponse.

	\begin{center}
		\psset{xunit=1.0cm,yunit=1.0cm,algebraic=true,dotstyle=o,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
		\begin{pspicture*}(-0.4,-0.6)(6.4,3.6)
		\psline(0,3)(0,0)
		\psline(0,0)(5,0)
		\psline(5,0)(5,3)
		\psline(5,3)(0,3)
		\psline(0,0)(1.66,3)
		\psline(0,3)(5,0)
		\psline(1.66,3)(5,1)
		\rput[bl](-0.28,3.08){$B$}
		\rput[bl](5.08,3.12){$L$}
		\rput[bl](5.14,-0.14){$E$}
		\rput[bl](-0.28,-0.14){$U$}
		\rput[bl](5.14,0.92){$R$}
		\rput[bl](1.74,3.12){$I$}
		\rput[bl](2,-0.4){5~cm}
		\psline{<-}(0,-0.3)(1.9,-0.3)
		\psline{->}(3,-0.3)(5,-0.3)
		\rput[bl](5.2,0.4){1~cm}
		\psline{<-}(5.6,0)(5.6,0.3)
		\psline{->}(5.6,0.6)(5.6,1)
		\rput[bl](5.2,2){2~cm}
		\psline{<-}(5.6,1)(5.6,1.9)
		\psline{->}(5.6,2.2)(5.6,3)
		\end{pspicture*}
	\end{center}
\end{frame}



\begin{frame}
	\frametitle{Petite longueur}
		Sur la figure ci-contre, les droites $(VU)$ et $(TS)$ sont parallèles. les longueurs sont données en cm.\\
		Calculer la longueur $VT$.
		\begin{center}
		\psset{xunit=1.0cm,yunit=1.0cm,algebraic=true,dotstyle=o,dotsize=3pt 0,linewidth=0.8pt,arrowsize=3pt 2,arrowinset=0.25}
		\begin{pspicture*}(-1,-2)(6,2)
		\psline(0,0)(3,1)
		\psline(3,1)(4.52,-1)
		\psline(4.52,-1)(0,0)
		\psline(2.01,0.67)(3.03,-0.67)
		\rput[bl](-0.32,-0.1){$R$}
		\rput[bl](3.08,1.12){$T$}
		\rput[bl](4.62,-1.28){$S$}
		\rput[bl](1.84,0.84){$V$}
		\rput[bl](2.9,-0.98){$U$}
		\rput[bl](2.6,0){1,5}
		\rput[bl](4,0){2,4}
		%\psline{<-}(0,0.2)(0.6,0.45)
		%\psline{->}(0.8,0.5)(1.8,0.8)
			\psline{<->}(0,0.2)(1.8,0.8)
			\rput[bl](0.6,0.5){2}
			\psline{<->}(2.1,0.9)(3,1.2)
			\rput[bl](2.4,1.2){?}
		\end{pspicture*}
	\end{center}
\end{frame}
\end{document}