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\usepackage{pst-plot,pst-tree,pstricks,pst-node,pstricks-add,pst-math,pst-xkey,pst-eucl}
\usepackage[francais]{babel} 
\everymath{\displaystyle}
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\begin{document}
%\tableofcontents

\begin{center}\section*{\textcolor{red}{2nde 6 : correction du TD (révisions)}}\end{center}
%Sources : https://www.capes-de-maths.com/3eme/Devoirs1011/Pythagore.pdf


\begin{multicols}{2}
\setlength{\columnseprule}{1pt}
\setlength{\columnsep}{2 cm}

\subsection{}
On considère le triangle suivant :
\begin{center}
\psset{xunit=1cm,yunit=1cm,comma=true,algebraic=true}
\begin{pspicture}(-0.5,-0.5)(6,4)
\pstGeonode(0,0){G}
\pstGeonode[PosAngle=90](0,3.245){Z}
\pstGeonode[PosAngle=90](5.4,3.245){A}
\pstRightAngle{G}{Z}{A}
\pstLineAB{G}{Z}
\pstLineAB{A}{Z}
\pstLineAB{G}{A}
\pstLabelAB{Z}{A}{5,4 cm}
\pstLabelAB{G}{A}{6,3 cm}
\end{pspicture}
\end{center}
Calculer la longueur GZ.

\subsection{}
On considère la figure suivante :\psset{xunit=2cm,yunit=2cm,comma=true,algebraic=true}
\begin{center}
\begin{pspicture}(-0.5,-0.5)(3,1.5)
\pstGeonode[PosAngle=180](0,0){A}
\pstGeonode[PosAngle=-90](1,0){C}\pstGeonode[PosAngle=0](2,1){D}\pstGeonode[PosAngle=135](0,1){B}
\pstSegmentMark[SegmentSymbol=pstslash]{A}{B}
\pstSegmentMark[SegmentSymbol=pstslash]{A}{C}
\pstSegmentMark[SegmentSymbol=pstslashh]{C}{D}
\pstSegmentMark[SegmentSymbol=pstslashh]{C}{B}
\pstLineAB{B}{D}
\pstLabelAB[nrot=:D]{C}{A}{1 cm}
\pstRightAngle[RightAngleSize=0.2]{C}{A}{B}
\pstRightAngle[RightAngleSize=0.2]{D}{C}{B}

\end{pspicture}
\end{center}
Calculer la longueur BD.

\subsection{}
Soit le triangle $FOU$ tel que : $FU=13$, $FO=12$ et $OU=5$.\\
Ce triangle est-il rectangle ?

\subsection{}
On considère la figure suivante.
\begin{center}
\psset{xunit=0.5,yunit=0.5,comma=true,algebraic=true}
\begin{pspicture}(-1,-1)(7,6)
%\psaxes[linewidth=1.25pt,Dx=1,Dy=1]{->}(0,0)()()
\psgrid[subgriddiv=1,gridlabels=0](0,0)(6,5)
\pstGeonode[PosAngle=-90](1,0){R}
\pstGeonode[PosAngle=180](0,3){C}
\pstGeonode[PosAngle=45](0,0){S}
\pstGeonode[PosAngle=45](6,5){A}
\pstGeonode[PosAngle=-135](0,0){S}\pstGeonode[PosAngle=0](6,0){Z}\pstGeonode[PosAngle=135](0,5){T}
\pstLineAB[linewidth=2pt]{R}{A}
\pstLineAB[linewidth=2pt]{A}{C}
\pstLineAB[linewidth=2pt]{C}{R}
\end{pspicture}

\end{center}
Le triangle $RAC$ est-il rectangle ?

\subsection{}
On considère la figure suivante :
\begin{center}
\psset{xunit=1cm,yunit=1cm,comma=true,algebraic=true}
\begin{pspicture}(-0.5,-0.5)(7.5,5.5)
\pstGeonode[PosAngle=180](0,0){B}
\pstGeonode[PosAngle=-90](4,0){H}\pstGeonode[PosAngle=-90](7,0){C}\pstGeonode[PosAngle=90](4,5){A}
\pstLineAB{B}{C}\pstLineAB{A}{C}\pstLineAB{B}{A}\pstLineAB{A}{H}
\pstLabelAB[nrot=:D]{H}{B}{4}\pstLabelAB[nrot=:D]{C}{H}{3}
\pstLabelAB{A}{C}{6}\pstLabelAB{A}{H}{5}
\end{pspicture}
\end{center}
La droite $(AH)$ est-elle une hauteur du triangle $ABC$ ?

\end{multicols}

\label{fin}
\end{document}  