--- /dev/null
+%=========================================\r
+%Macros personnelles\r
+%christophe.poulain@melusine.eu.org\r
+%création : 25 Septembre 1999\r
+%dernière modification : 28 Avril 2005\r
+%=========================================\r
+\r
+\RequirePackage{xlop,fancybox,color,ifthen,amssymb}\r
+\input{xlopsqrt}\r
+\newtheorem{ppte}{Propri\'et\'e}\r
+\newtheorem{theo}{Th\'eor\`eme}\r
+\newtheorem{defi}{D\'efinition}\r
+\newtheorem{lemme}{Lemme}\r
+\newtheorem{coro}{Corollaire}\r
+\newtheorem{prop}{Proposition}\r
+\newtheorem{reg}{R\`egle}\r
+\newtheorem{conj}{Conjecture}\r
+\newtheorem{remar}{Remarque}\r
+\newtheorem{exem}{Exemple}\r
+\r
+\newcommand{\rema}{\underline{Remarque} }\r
+\newcommand{\exe}{\underline{Exemple} }\r
+\newcommand{\pre}{\underline{Preuve}}\r
+\newcommand{\cas}{\underline{Cas particulier}}\r
+\newcommand{\cass}{\underline{Cas particuliers}}\r
+\newcommand{\Not}{\underline{Notation} }\r
+\newcommand{\Si}{\underline{Si} }\r
+\newcommand{\si}{\underline{si} }\r
+\newcommand{\alors}{\underline{alors} }\r
+\newcommand{\cons}{\underline{Conséquence}}\r
+\newcommand{\Comme}{\underline{Comme} }\r
+\newcommand{\comme}{\underline{comme} }\r
+\r
+\def\qed{\hfill\raise -2pt\hbox{\vrule\vbox to 10pt{\hrule width4pt\vfill\hrule}\vrule}}\r
+\def\cqfd{\hfill\unskip\kern 6pt\penalty 500\qed\par}\r
+\r
+\catcode`\@=11\r
+\def\Eqalign#1{\null\,\vcenter{\openup\jot\m@th\ialign{\r
+\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\hfil\r
+&&\quad\strut\hfil$\displaystyle{##}$&$\displaystyle{{}##}$\r
+\hfil\crcr #1\crcr}}\,}\r
+\catcode`\@=12\r
+\r
+\newcommand{\vecteur}[1]\r
+{\overrightarrow{\strut #1}}\r
+\r
+\font\tenbb=msbm10\r
+\font\sevenbb=msbm7\r
+\font\fivebb=msbm5\r
+\newfam\bbfam\r
+\textfont\bbfam=\tenbb\r
+\scriptfont\bbfam=\sevenbb\r
+\scriptscriptfont\bbfam=\fivebb\r
+\def\bb{\fam\bbfam\tenbb}\r
+\let\oldbb=\bb\r
+\def\bb #1{{\oldbb #1}}\r
+\r
+\def\tvi{\vrule height 12pt depth 5pt width 0pt}\r
+\def\tvj{\vrule height 12pt depth 5pt width 1pt}\r
+\def\hfq{\hfill\,\,}\r
+\def\cc#1{\hfq #1\hfq}\r
+\def\tv{\tvi\vrule}\r
+\def\tw{\tvj\vrule}\r
+\def\traithorizontal{\noalign{\hrule}}\r
+\def\traithorizontale{\noalign{\hrule height 1pt}}\r
+\r
+\newcommand{\encadre}[1]\r
+{\begin{center}\r
+\fbox{\begin{minipage}{\linewidth}\r
+{#1}\r
+\end{minipage}}\r
+\end{center}\r
+}\r
+\r
+\def\pgcd{\mathop{\rm PGCD}\nolimits}\r
+\def\ppcm{\mathop{\rm PPCM}\nolimits}\r
+\r
+\def\cut{{}\hfill\cr \hfill{}}\r
+\r
+\newcommand{\biindice}[3]%\r
+{\r
+\renewcommand{\arraystretch}{0.5}\r
+\begin{array}[t]{c}\r
+#1\\\r
+{\scriptstyle #2}\\\r
+{\scriptstyle #3}\r
+\end{array}\r
+\renewcommand{\arraystretch}{1}\r
+}\r
+\r
+\newlength{\ltxt}\r
+\newcommand{\compo}[4]{\r
+\setlength{\ltxt}{\linewidth}\r
+\setbox#1=\hbox{\includegraphics[scale=#3]{#2.#1}}\r
+\addtolength{\ltxt}{-\wd#1}\r
+\addtolength{\ltxt}{-10pt}\r
+\begin{minipage}{\wd#1}\r
+\includegraphics[scale=#3]{#2.#1}\r
+\end{minipage}\r
+\hfill\r
+\begin{minipage}{\ltxt}\r
+#4\r
+\end{minipage}\r
+}\r
+\r
+\newlength{\lntxt}\r
+\newcommand{\Compo}[4]{\r
+\setlength{\lntxt}{\linewidth}\r
+\setbox#1=\hbox{\includegraphics[scale=#3]{#2}}\r
+\addtolength{\lntxt}{-\wd#1}\r
+\addtolength{\lntxt}{-10pt}\r
+\begin{minipage}{\wd#1}\r
+\includegraphics[scale=#3]{#2}\r
+\end{minipage}\r
+\hfill\r
+\begin{minipage}{\lntxt}\r
+#4\r
+\end{minipage}\r
+}\r
+\r
+\newcommand{\Compog}[4]{\r
+\setlength{\lntxt}{\linewidth}\r
+\setbox#1=\hbox{\includegraphics[scale=#3]{#2}}\r
+\addtolength{\lntxt}{-\wd#1}\r
+\addtolength{\lntxt}{-10pt}\r
+\begin{minipage}{\lntxt}\r
+#4\r
+\end{minipage}\r
+\hfill\r
+\begin{minipage}{\wd#1}\r
+\includegraphics[scale=#3]{#2}\r
+\end{minipage}\r
+}\r
+\r
+\newlength{\ecart}\r
+\setlength{\ecart}{-20pt}\r
+\r
+\newcommand{\compog}[4]{%\r
+\setlength{\ltxt}{\linewidth}\r
+\setbox#1=\hbox{\includegraphics[scale=#3]{#2.#1}}\r
+\addtolength{\ltxt}{-\wd#1}\r
+\addtolength{\ltxt}{\ecart}\r
+\begin{minipage}{\ltxt}\r
+#4\r
+\end{minipage}\r
+\hfill\r
+\begin{minipage}{\wd#1}\r
+\includegraphics[scale=#3]{#2.#1}\r
+\end{minipage}\r
+}\r
+\r
+\newlength{\appui}\r
+\setlength{\appui}{-20pt}\r
+\r
+\newlength{\lnttxt}\r
+\newcommand{\dispo}[3]{\r
+\setlength{\lnttxt}{\linewidth}\r
+\setbox#1=\hbox{#2}\r
+\addtolength{\lnttxt}{-\wd#1}\r
+\addtolength{\lnttxt}{\appui}\r
+\begin{minipage}{\wd#1}\r
+#2\r
+\end{minipage}\r
+\hfill\r
+\begin{minipage}{\lnttxt}\r
+#3\r
+\end{minipage}\r
+}\r
+\r
+\newcommand{\dispog}[3]{\r
+\setlength{\lnttxt}{\linewidth}\r
+\setbox#1=\hbox{#2}\r
+\addtolength{\lnttxt}{-\wd#1}\r
+\addtolength{\lnttxt}{\appui}\r
+\begin{minipage}{\lnttxt}\r
+#3\r
+\end{minipage}\r
+\hfill\r
+\begin{minipage}{\wd#1}\r
+#2\r
+\end{minipage}\r
+}\r
+\r
+\newcounter{num}[section]\r
+\newcommand{\exo}{\addtocounter{num}{1}\r
+\par\underline{\bf Exercice~\thenum} }\r
+\r
+\newcommand{\titrage}[2]{\r
+{\Large #1}\hfill#2\r
+\par\rule[+6pt]{\linewidth}{0.5mm}\r
+\par\r
+}\r
+\r
+\newcommand{\titragedossier}[1]{\r
+{\small #1}\hfill{\small www.melusine.eu.org/syracuse/poulecl/}\r
+\par\rule[+6pt]{\linewidth}{0.5mm}\r
+\par\r
+}\r
+\r
+\newcommand{\partie}[2]{\r
+\begin{center}\r
+\begin{minipage}{#1pt}\r
+\begin{center}\r
+\boxput*(0,0){\colorbox{white}{#2}}\r
+{\rule{\linewidth}{0.5mm}}\r
+\end{center}\r
+\end{minipage}\r
+\end{center}\r
+\par\r
+}\r
+\r
+\newenvironment{myenumerate}{\r
+\renewcommand{\theenumi}{\arabic{enumi}}\r
+\def\labelenumi{{\bf \theenumi /}}\r
+\begin{enumerate}}{\end{enumerate}}\r
+\r
+\newenvironment{Myenumerate}{\r
+\renewcommand{\theenumi}{\arabic{enumi}}\r
+\def\labelenumi{$\rhd${\bf \theenumi /}}\r
+\begin{enumerate}}{\end{enumerate}}\r
+\r
+\newenvironment{Enumerate}{\r
+\renewcommand{\theenumi}{\arabic{enumi}}\r
+\def\labelenumi{\textbf{\theenumi.}$\blacktriangleright$}\r
+\begin{enumerate}}{\end{enumerate}}\r
+\r
+\newdimen\shadeshift\shadeshift=1pt\r
+\def\shadedtext#1{{\setbox0=\hbox{#1}\leavevmode\r
+ \vtop to 0pt{\rlap{\special{color push rgb 0.75 0.75 0.75}%\r
+ \kern0.1em\lower0.1em\copy0\r
+ \special{color pop}}\vss}\box0}}%\r
+\long\def\shadedparagraph#1\par{{\setbox0=\vbox{\hsize=\hsize#1}%\r
+ \noindent\leavevmode\r
+ \vtop to 0pt{\rlap{\special{color push rgb 0.75 0.75 0.75}%\r
+ \kern0.1em\lower0.1em\copy0\r
+ \special{color pop}}\vss}\box0\par}}%\r
+\r
+\newboolean{exact}\r
+\setboolean{exact}{true}\r
+\newboolean{racine}\r
+\setboolean{racine}{false}\r
+\r
+\opcopy{2}{pres}\r
+\r
+\newcommand{\pythahypo}[5]{%\r
+\opset{decimalsepsymbol={,}}%\r
+\opcopy{#4}{A1}%\r
+\opcopy{#5}{A2}%\r
+Dans le triangle $#1#2#3$ rectangle en $#2$, le th\'eor\`eme de Pythagore permet d'\'ecrire :%\r
+\[\Eqalign{\r
+#1#3^2&=#1#2^2+#2#3^2\cr\r
+#1#3^2&=\opprint{A1}^2+\opprint{A2}^2\cr\r
+#1#3^2&=\opmul*{A1}{A1}{a1}\opprint{a1}+\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#3^2&=\opadd*{a1}{a2}{a3}\opprint{a3}\cr\r
+#1#3&=\sqrt{\opprint{a3}}\cr\r
+\ifthenelse{\boolean{racine}}{}{\ifthenelse{\boolean{exact}}{#1#3&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opprint{a4}}{#1#3&\approx\opsqrt[maxdivstep=3]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\r
+\opprint{a4}}}\cr\r
+}\]\r
+}\r
+\r
+\newcommand{\egapythahypo}[5]{%\r
+\opset{decimalsepsymbol={,}}%\r
+\opcopy{#4}{A1}%\r
+\opcopy{#5}{A2}%\r
+Comme le triangle $#1#2#3$ est rectangle en $#2$, alors l'égalité de\r
+Pythagore est vérifiée :\r
+\[\Eqalign{\r
+#1#3^2&=#1#2^2+#2#3^2\cr\r
+#1#3^2&=\opprint{A1}^2+\opprint{A2}^2\cr\r
+#1#3^2&=\opmul*{A1}{A1}{a1}\opprint{a1}+\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#3^2&=\opadd*{a1}{a2}{a3}\opprint{a3}\cr\r
+#1#3&=\sqrt{\opprint{a3}}\cr\r
+\ifthenelse{\boolean{racine}}{}{\ifthenelse{\boolean{exact}}{#1#3&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opprint{a4}}{#1#3&\approx\opsqrt[maxdivstep=3]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\r
+\opprint{a4}}}\cr\r
+}\]\r
+}\r
+\r
+\newcommand{\egapythahyposansrac}[5]{%\r
+\opset{decimalsepsymbol={,}}%\r
+\opcopy{#4}{A1}%\r
+\opcopy{#5}{A2}%\r
+Comme le triangle $#1#2#3$ est rectangle en $#2$, alors l'égalité de\r
+Pythagore est vérifiée :\r
+\[\Eqalign{\r
+#1#3^2&=#1#2^2+#2#3^2\cr\r
+#1#3^2&=\opprint{A1}^2+\opprint{A2}^2\cr\r
+#1#3^2&=\opmul*{A1}{A1}{a1}\opprint{a1}+\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#3^2&=\opadd*{a1}{a2}{a3}\opprint{a3}\cr\r
+\ifthenelse{\boolean{racine}}{}{\ifthenelse{\boolean{exact}}{#1#3&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opprint{a4}}{#1#3&\approx\opsqrt[maxdivstep=3]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\r
+\opprint{a4}}}\cr\r
+}\]\r
+}\r
+\r
+\newcommand{\egapythahyposansracd}[5]{%\r
+\opset{decimalsepsymbol={,}}%\r
+\opcopy{#4}{A1}%\r
+\opcopy{#5}{A2}%\r
+Le triangle $#1#2#3$ est rectangle en $#2$ donc l'égalité de\r
+Pythagore est vérifiée :\r
+\[\Eqalign{\r
+#1#3^2&=#1#2^2+#2#3^2\cr\r
+#1#3^2&=\opprint{A1}^2+\opprint{A2}^2\cr\r
+#1#3^2&=\opmul*{A1}{A1}{a1}\opprint{a1}+\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#3^2&=\opadd*{a1}{a2}{a3}\opprint{a3}\cr\r
+\ifthenelse{\boolean{racine}}{}{\ifthenelse{\boolean{exact}}{#1#3&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opprint{a4}}{#1#3&\approx\opsqrt[maxdivstep=3]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\r
+\opprint{a4}}}\cr\r
+}\]\r
+}\r
+\r
+\newcommand{\egapythahypod}[5]{%\r
+\opset{decimalsepsymbol={,}}%\r
+\opcopy{#4}{A1}%\r
+\opcopy{#5}{A2}%\r
+Le triangle $#1#2#3$ est rectangle en $#2$ donc l'égalité de\r
+Pythagore est vérifiée :\r
+\[\Eqalign{\r
+#1#3^2&=#1#2^2+#2#3^2\cr\r
+#1#3^2&=\opprint{A1}^2+\opprint{A2}^2\cr\r
+#1#3^2&=\opmul*{A1}{A1}{a1}\opprint{a1}+\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#3^2&=\opadd*{a1}{a2}{a3}\opprint{a3}\cr\r
+#1#3&=\sqrt{\opprint{a3}}\cr\r
+\ifthenelse{\boolean{racine}}{}{\ifthenelse{\boolean{exact}}{#1#3&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opprint{a4}}{#1#3&\approx\opsqrt[maxdivstep=3]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\r
+\opprint{a4}}}\cr\r
+}\]\r
+}\r
+\r
+\newcommand{\pythadroit}[5]{\r
+\opset{decimalsepsymbol={,}}\r
+\opcopy{#4}{A1}\r
+\opcopy{#5}{A2}\r
+Dans le triangle $#1#2#3$ rectangle en $#2$, le théorème de Pythagore permet d'écrire :\r
+\[\Eqalign{\r
+#1#3^2&=#1#2^2+#2#3^2\cr\r
+\opprint{A1}^2&=#1#2^2+\opprint{A2}^2\cr\r
+\opmul*{A1}{A1}{a1}\opprint{a1}&=#1#2^2+\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#2^2&=\opmul*{A1}{A1}{a1}\opprint{a1}-\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#2^2&=\opsub*{a1}{a2}{a3}\opprint{a3}\cr\r
+#1#2&=\sqrt{\opprint{a3}}\cr\r
+\ifthenelse{\boolean{racine}}{}{\ifthenelse{\boolean{exact}}{#1#2&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opprint{a4}}{#1#2&\approx\opsqrt[maxdivstep=3]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\r
+\opprint{a4}}}\cr\r
+}\]\r
+}\r
+\r
+\newcommand{\egapythadroit}[5]{%\r
+\opset{decimalsepsymbol={,}}%\r
+\opcopy{#4}{A1}%\r
+\opcopy{#5}{A2}%\r
+Comme le triangle $#1#2#3$ est rectangle en $#2$, alors l'égalité de %\r
+Pythagore est vérifiée :%\r
+\[\Eqalign{\r
+#1#3^2&=#1#2^2+#2#3^2\cr\r
+\opprint{A1}^2&=#1#2^2+\opprint{A2}^2\cr\r
+\opmul*{A1}{A1}{a1}\opprint{a1}&=#1#2^2+\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#2^2&=\opmul*{A1}{A1}{a1}\opprint{a1}-\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#2^2&=\opsub*{a1}{a2}{a3}\opprint{a3}\cr\r
+#1#2&=\sqrt{\opprint{a3}}\cr\r
+\ifthenelse{\boolean{racine}}{}{\ifthenelse{\boolean{exact}}{#1#2&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opprint{a4}}{#1#2&\approx\opsqrt[maxdivstep=3]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\r
+\opprint{a4}}}\cr\r
+}\]\r
+}\r
+\r
+\newcommand{\egapythadroitsansrac}[5]{%\r
+\opset{decimalsepsymbol={,}}%\r
+\opcopy{#4}{A1}%\r
+\opcopy{#5}{A2}%\r
+Comme le triangle $#1#2#3$ est rectangle en $#2$ alors l'égalité de %\r
+Pythagore est vérifiée :%\r
+\[\Eqalign{\r
+#1#3^2&=#1#2^2+#2#3^2\cr\r
+\opprint{A1}^2&=#1#2^2+\opprint{A2}^2\cr\r
+\opmul*{A1}{A1}{a1}\opprint{a1}&=#1#2^2+\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#2^2&=\opmul*{A1}{A1}{a1}\opprint{a1}-\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#2^2&=\opsub*{a1}{a2}{a3}\opprint{a3}\cr\r
+\ifthenelse{\boolean{racine}}{}{\ifthenelse{\boolean{exact}}{#1#2&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opprint{a4}}{#1#2&\approx\opsqrt[maxdivstep=3]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\r
+\opprint{a4}}}\cr\r
+}\]\r
+}\r
+\r
+\newcommand{\egapythadroitd}[5]{%\r
+\opset{decimalsepsymbol={,}}%\r
+\opcopy{#4}{A1}%\r
+\opcopy{#5}{A2}%\r
+Le triangle $#1#2#3$ est rectangle en $#2$ donc l'égalité de %\r
+Pythagore est vérifiée :\r
+\[\Eqalign{\r
+#1#3^2&=#1#2^2+#2#3^2\cr\r
+\opprint{A1}^2&=#1#2^2+\opprint{A2}^2\cr\r
+\opmul*{A1}{A1}{a1}\opprint{a1}&=#1#2^2+\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#2^2&=\opmul*{A1}{A1}{a1}\opprint{a1}-\opmul*{A2}{A2}{a2}\opprint{a2}\cr\r
+#1#2^2&=\opsub*{a1}{a2}{a3}\opprint{a3}\cr\r
+#1#2&=\sqrt{\opprint{a3}}\cr\r
+\ifthenelse{\boolean{racine}}{}{\ifthenelse{\boolean{exact}}{#1#2&=\opsqrt[maxdivstep=3]{a3}{a4}\opunzero{a4}\opprint{a4}}{#1#2&\approx\opsqrt[maxdivstep=3]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\r
+\opprint{a4}}}\cr\r
+}\]\r
+}\r
+\r
+\newcommand{\Recipytha}[6]{\r
+\opset{decimalsepsymbol={,}}\r
+\opcopy{#4}{A1}\r
+\opcopy{#5}{A2}\r
+\opcopy{#6}{A3}\r
+Dans le triangle $#1#2#3$, $[#1#3]$ est le plus grand côté.\r
+\[\left.\r
+ \begin{array}{l}\r
+ #1#3^2=\opprint{A1}^2=\opmul*{A1}{A1}{a1}\opprint{a1}\cr\r
+ #1#2^2+#2#3^2=\opprint{A2}^2+\opprint{A3}^2=\opmul*{A2}{A2}{a2}\opprint{a2}+\opmul*{A3}{A3}{a3}\opprint{a3}=\opadd*{a2}{a3}{a4}\opprint{a4}\cr\r
+ \end{array}\r
+\right\}#1#3^2=#1#2^2+#2#3^2\r
+\]\r
+Comme $#1#3^2=#1#2^2+#2#3^2$ alors le triangle $#1#2#3$ est rectangle\r
+en $#2$ d'après la réciproque du théorème de Pythagore.}\r
+\r
+\newcommand{\Reciegapytha}[6]{\r
+\opset{decimalsepsymbol={,}}\r
+\opcopy{#4}{A1}\r
+\opcopy{#5}{A2}\r
+\opcopy{#6}{A3}\r
+Dans le triangle $#1#2#3$, $[#1#3]$ est le plus grand côté.\r
+\[\left.\r
+ \begin{array}{l}\r
+ #1#3^2=\opprint{A1}^2=\opmul*{A1}{A1}{a1}\opprint{a1}\cr\r
+ #1#2^2+#2#3^2=\opprint{A2}^2+\opprint{A3}^2=\opmul*{A2}{A2}{a2}\opprint{a2}+\opmul*{A3}{A3}{a3}\opprint{a3}=\opadd*{a2}{a3}{a4}\opprint{a4}\cr\r
+ \end{array}\r
+\right\}#1#3^2=#1#2^2+#2#3^2\r
+\]\r
+L'égalité de Pythagore est vérifiée donc le triangle $#1#2#3$ est rectangle en $#2$.}\r
+\r
+\newcommand{\Recipythacol}[6]{\r
+\opset{decimalsepsymbol={,}}\r
+\opcopy{#4}{A1}\r
+\opcopy{#5}{A2}\r
+\opcopy{#6}{A3}\r
+Dans le triangle $#1#2#3$, $[#1#3]$ est le plus grand côté.\r
+\[\Eqalign{\r
+ #1#3^2&\kern0.15\linewidth#2^2+#2#3^2\cr\r
+ \opprint{A1}^2&&\opprint{A2}^2+\opprint{A3}^2\cr\r
+ \opmul*{A1}{A1}{a1}\opprint{a1}&&\opmul*{A2}{A2}{a2}\opprint{a2}+\opmul*{A3}{A3}{a3}\opprint{a3}\cr\r
+ &&\opadd*{a2}{a3}{a4}\opprint{a4}\cr\r
+}\]\r
+Comme $#1#3^2=#1#2^2+#2#3^2$ alors le triangle $#1#2#3$ est rectangle\r
+en $#2$ d'après la réciproque du théorème de Pythagore.}\r
+\r
+\newcommand{\Reciegapythacol}[6]{\r
+\opset{decimalsepsymbol={,}}\r
+\opcopy{#4}{A1}\r
+\opcopy{#5}{A2}\r
+\opcopy{#6}{A3}\r
+Dans le triangle $#1#2#3$, $[#1#3]$ est le plus grand côté.\r
+\[\Eqalign{\r
+ #1#3^2&\kern0.15\linewidth#2^2+#2#3^2\cr\r
+ \opprint{A1}^2&&\opprint{A2}^2+\opprint{A3}^2\cr\r
+ \opmul*{A1}{A1}{a1}\opprint{a1}&&\opmul*{A2}{A2}{a2}\opprint{a2}+\opmul*{A3}{A3}{a3}\opprint{a3}\cr\r
+ &&\opadd*{a2}{a3}{a4}\opprint{a4}\cr\r
+}\]\r
+Comme l'égalité de Pythagore est vérifiée alors le triangle $#1#2#3$ est rectangle en $#2$.}\r
+\r
+\newcommand{\Thales}[5]{%\r
+Dans le triangle $#1#2#3$, $#4$ est un point de la\r
+ droite $(#1#2)$, $#5$ est un point de la droite\r
+ $(#1#3)$ ; les droites $(#4#5)$ et $(#2#3)$ sont parallèles.\r
+ Le théorème de Thalès permet d'écrire :\r
+\[\frac{#1#4}{#1#2}=\frac{#1#5}{#1#3}=\frac{#4#5}{#2#3}\]%\r
+}\r
+\r
+\newcommand{\Thalesd}[5]{%\r
+Dans le triangle $#1#2#3$, $#4$ appartient à la\r
+ droite $(#1#2)$, $#5$ appartient à la droite\r
+ $(#1#3)$. Comme les droites $(#4#5)$ et $(#2#3)$ sont parallèles\r
+ alors le théorème de Thalès permet d'écrire :\r
+\[\frac{#1#4}{#1#2}=\frac{#1#5}{#1#3}=\frac{#4#5}{#2#3}\]%\r
+}\r
+\r
+\newcommand{\Thalesa}[5]{%\r
+Dans le triangle $#1#2#3$, $#4$ appartient à la\r
+ droite $(#1#2)$, $#5$ appartient à la droite\r
+ $(#1#3)$ ; les droites $(#4#5)$ et $(#2#3)$ sont parallèles.\r
+ Le théorème de Thalès permet d'écrire :\r
+\[\frac{#1#4}{#1#2}=\frac{#1#5}{#1#3}=\frac{#4#5}{#2#3}\]%\r
+}\r
+\r
+\newcommand{\Thalesf}[5]{\r
+Dans le triangle $#1#2#3$, $#4$ est un point du\r
+ segment $[#1#2]$, $#5$ est un point du segment\r
+ $[#1#3]$ ; les droites $(#4#5)$ et $(#2#3)$ sont parallèles.\r
+ L'égalité des 3 rapports permet d'écrire :\r
+\[\frac{#1#4}{#1#2}=\frac{#1#5}{#1#3}=\frac{#4#5}{#2#3}\]\r
+}\r
+\r
+\newcommand{\ThalesF}[5]{\r
+Dans le triangle $#1#2#3$, $#4$ est un point du\r
+ segment $[#1#2]$, $#5$ est un point du segment\r
+ $[#1#3]$. Comme les droites $(#4#5)$ et $(#2#3)$ sont parallèles\r
+ alors, d'après l'égalité des trois rapports, on a :\r
+\[\frac{#1#4}{#1#2}=\frac{#1#5}{#1#3}=\frac{#4#5}{#2#3}.\]\r
+}\r
+\r
+\newcommand{\ResolThales}[6]{%\r
+\opset{decimalsepsymbol={,}}%\r
+\opcopy{#3}{a3}%\r
+\opcopy{#4}{a4}%\r
+\opcopy{#5}{a5}%\r
+On utilise %\r
+\[\Eqalign{%\r
+\frac{#1#2}{\opprint{a3}}&=\frac{\opprint{a4}}{\opprint{a5}}\cr%\r
+#1#2&=\frac{\opprint{a3}\times\opprint{a4}}{\opprint{a5}}\cr%\r
+#1#2&=\frac{\opmul*{a3}{a4}{a6}\opunzero{a6}\opprint{a6}}{\opprint{a5}}\cr%\r
+\ifthenelse{\boolean{exact}}{#1#2&=\opdiv*[maxdivstep=4]{a6}{a5}{a7}{a8}\opunzero{a7}\opprint{a7}\cr}{#1#2&\approx\opdiv*[maxdivstep=4]{a6}{a5}{a7}{a8}\opunzero{a7}\opprint{a7}\cr}%\r
+}\]%\r
+\ifthenelse{\boolean{exact}}{La longueur $#1#2$ mesure \opprint{a7}\,#6}{La longueur $#1#2$ mesure environ \opprint{a7}\,#6}%\r
+}\r
+\r
+%%QCM\r
+\newcounter{qqcm}\r
+\r
+%définir un booléen qui permet de choisir la correction ou non\r
+\newboolean{solution}\r
+\r
+%définir une commande \V qui permet de changer le carré en carré coché suivant la valeur du booléen.\r
+\newcommand{\V}[1]{\ifthenelse{\boolean{solution}}{$\boxtimes$\kern2mm #1}{$\Box$\kern2mm #1}}\r
+\newcommand{\F}[1]{$\Box$\kern2mm #1}\r
+\newcommand{\vr}{\ifthenelse{\boolean{solution}}{$\boxtimes$}{$\Box$}}\r
+\newcommand{\fa}{$\Box$}\r
+\r
+%%QCM Version 2\r
+\newenvironment{Qcm}[1][2]{\par\setboolean{solution}{false}\r
+\setcounter{qqcm}{0}\renewcommand{\arraystretch}{1.5}\r
+\begin{tabular}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}b{\linewidth/#1}|*{#1}{l|}}\hline}{\hline\end{tabular}\r
+\renewcommand{\arraystretch}{1}}\r
+\r
+\newenvironment{Qcmcor}[1][2]{\par\setboolean{solution}{true}\setcounter{qqcm}{0}\renewcommand{\arraystretch}{1.5}\r
+\begin{tabular}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}b{\linewidth/#1}|*{#1}{l|}}\hline}{\hline\end{tabular}\r
+\renewcommand{\arraystretch}{1}}\r
+\r
+\newcounter{taill}\r
+\newcommand{\QCM}[3]{\setboolean{solution}{false}\r
+\setcounter{qqcm}{0}\r
+\renewcommand{\arraystretch}{1.5}\r
+\setcounter{taill}{#1}\r
+\addtocounter{taill}{1}\r
+\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}X|*{#1}{l|}}\r
+\hline\r
+\multicolumn{\thetaill}{|c|}{{\sc #2}}\\\r
+#3\r
+\hline\r
+\end{tabularx}\r
+\renewcommand{\arraystretch}{1}\r
+}\r
+\r
+\newcommand{\QCMcor}[3]{\setboolean{solution}{true}\r
+\setcounter{qqcm}{0}\r
+\renewcommand{\arraystretch}{1.5}\r
+\setcounter{taill}{#1}\r
+\addtocounter{taill}{1}\r
+\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}X|*{#1}{l|}}\r
+\hline\r
+\multicolumn{\thetaill}{|c|}{{\sc #2}}\\\r
+#3\r
+\hline\r
+\end{tabularx}\r
+\renewcommand{\arraystretch}{1}\r
+}\r
+\r
+\newcommand{\QCMvar}[4]{\setboolean{solution}{false}\r
+\setcounter{qqcm}{0}\r
+\renewcommand{\arraystretch}{#2}\r
+\setcounter{taill}{#1}\r
+\addtocounter{taill}{1}\r
+\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}X|*{#1}{l|}}\r
+\hline\r
+\multicolumn{\thetaill}{|c|}{{\sc #3}}\\\r
+#4\r
+\hline\r
+\end{tabularx}\r
+\renewcommand{\arraystretch}{1}%\r
+}\r
+\r
+\newcommand{\QCMvarcor}[4]{\setboolean{solution}{true}\r
+\setcounter{qqcm}{0}\r
+\renewcommand{\arraystretch}{#2}\r
+\setcounter{taill}{#1}\r
+\addtocounter{taill}{1}\r
+\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}X|*{#1}{l|}}\r
+\hline\r
+\multicolumn{\thetaill}{|c|}{{\sc #3}}\\\r
+#4\r
+\hline\r
+\end{tabularx}\r
+\renewcommand{\arraystretch}{1}\r
+}\r
+\r
+\newenvironment{VF}[1]{\par\setboolean{solution}{false}\r
+\setcounter{qqcm}{0}\renewcommand{\arraystretch}{1.5}\r
+\begin{center}\r
+\begin{tabular}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}b{\linewidth/2}|*{2}{c|}}\hline\r
+\multicolumn{3}{|c|}{#1}\\\r
+\hline\r
+\multicolumn{1}{|c|}{\bf Question}&\multicolumn{1}{c|}{\bf Vrai}&\multicolumn{1}{c|}{\bf Faux}\\\r
+\hline\r
+}{\hline\end{tabular}\r
+\end{center}\renewcommand{\arraystretch}{1}}\r
+\r
+\newenvironment{VFvar}[2]{\par\setboolean{solution}{false}\r
+\setcounter{qqcm}{0}\renewcommand{\arraystretch}{1.5}\r
+\begin{center}\r
+\begin{tabular}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}b{#2}|*{2}{c|}}\hline\r
+\multicolumn{3}{|c|}{#1}\\\r
+\hline\r
+\multicolumn{1}{|c|}{\bf Question}&\multicolumn{1}{c|}{\bf Vrai}&\multicolumn{1}{c|}{\bf Faux}\\\r
+\hline\r
+}{\hline\end{tabular}\r
+\end{center}\renewcommand{\arraystretch}{1}}\r
+\r
+\r
+\newenvironment{VFcor}[1]{\par\setboolean{solution}{true}\setcounter{qqcm}{0}\renewcommand{\arraystretch}{1.5}\r
+\begin{tabular}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}b{\linewidth/2}|*{2}{c|}}\hline\r
+\multicolumn{3}{|c|}{#1}\\\r
+\hline\r
+\multicolumn{1}{|c|}{\bf Question}&\multicolumn{1}{c|}{\bf Vrai}&\multicolumn{1}{c|}{\bf Faux}\\\r
+\hline\r
+}{\hline\end{tabular}\r
+\renewcommand{\arraystretch}{1}}\r
+\r
+\r
+\newcommand{\QCMsimple}[2]{\setboolean{solution}{false}\r
+\setcounter{qqcm}{0}\r
+\renewcommand{\arraystretch}{1.5}\r
+\setcounter{taill}{#1}\r
+\addtocounter{taill}{1}\r
+\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}X|*{#1}{l|}}\r
+\hline\r
+#2\r
+\hline\r
+\end{tabularx}\r
+\renewcommand{\arraystretch}{1}\r
+}\r
+\r
+\newcommand{\QCMsimplevar}[3]{\setboolean{solution}{false}\r
+\setcounter{qqcm}{0}\r
+\renewcommand{\arraystretch}{#2}\r
+\setcounter{taill}{#1}\r
+\addtocounter{taill}{1}\r
+\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm$\blacktriangleright$}\,}X|*{#1}{l|}}\r
+\hline\r
+#3\r
+\hline\r
+\end{tabularx}\r
+\renewcommand{\arraystretch}{1}\r
+}\r
+\r
+\newcommand{\QCMsimplecor}[2]{\setboolean{solution}{true}\r
+\setcounter{qqcm}{0}\r
+\renewcommand{\arraystretch}{1.5}\r
+\setcounter{taill}{#1}\r
+\addtocounter{taill}{1}\r
+\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm$\blacktriangleright$}\,}X|*{#1}{l|}}\r
+\hline\r
+#2\r
+\hline\r
+\end{tabularx}\r
+\renewcommand{\arraystretch}{1}\r
+}\r
+\r
+\newcommand{\QCMsimplevarcor}[3]{\setboolean{solution}{true}\r
+\setcounter{qqcm}{0}\r
+\renewcommand{\arraystretch}{#2}\r
+\setcounter{taill}{#1}\r
+\addtocounter{taill}{1}\r
+\begin{tabularx}{\linewidth}{|>{\small\stepcounter{qqcm}{\bf \theqqcm/}\,}X|*{#1}{l|}}\r
+\hline\r
+#3\r
+\hline\r
+\end{tabularx}\r
+\renewcommand{\arraystretch}{1}\r
+}
\ No newline at end of file
Projets / mp-solid.git / blobdiff
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