%@Auteur: François Meria\par \begin{multicols}{2} À partir de la figure 1 ci-contre, on veut obtenir la figure 2 puis la figure 3, uniquement à l'aide de la symétrie axiale. \begin{center} \psset{unit=1cm} \pspicture(-2,-0.5)(5,2.2) \rput{25}{ \pstGeonode[PointSymbol=none,PosAngle={-45,-45,-45,-45,-45,-45,90}](0,0){O}(1,0){I}(2,0){J}(3,0){K}(4,0){L}(5,0){M}(0,2){A} \pstSegmentMark[SegmentSymbol=pstslashh]{O}{I} \pstSegmentMark[SegmentSymbol=pstslashh]{I}{J} \pstSegmentMark[SegmentSymbol=pstslashh]{J}{K} \pstSegmentMark[SegmentSymbol=pstslashh]{K}{L} \pstSegmentMark[SegmentSymbol=pstslashh]{L}{M} \pstLineAB{A}{O} \pstLineAB{A}{I} \pstLineAB{A}{J} \pstLineAB{A}{K} \pstLineAB{A}{L} \pstLineAB{A}{M} } \put(2,0){Figure 1} \endpspicture \end{center} \end{multicols} \begin{enumerate}[(a)] \item Reproduire la figure 1 en prenant $OA=2$~cm et $OI=1$~cm. \item Quels sont les axes de symétrie de la figure 2 ? Compléter la figure 1 afin d'obtenir la figure 2. \item Décrire avec précision les axes de symétrie de la figure 3. Compléter la figure 2 pour obtenir la figure 3. \item Colorier la figure 3 à l'aide de deux couleurs en alternant les couleurs. \item Combien d'axes de symétrie possède la figure 3 ? Et la figure coloriée ? \end{enumerate} \begin{center} \psset{unit=1cm} \pspicture(-5,-3)(5,2.5) \rput{25}{ \pstGeonode[PointSymbol=none,PosAngle={-40,-40,-40,-40,-40,-40,90}](0,0){O}(1,0){I}(2,0){J}(3,0){K}(4,0){L}(5,0){M}(0,2){A} \pstLineAB{A}{O} \pstLineAB{A}{I} \pstLineAB{A}{J} \pstLineAB{A}{K} \pstLineAB{A}{L} \pstLineAB{A}{M} \pstLineAB{O}{M} \pstOrtSym[PointSymbol=none,PosAngle=-45]{O}{M}{A}[B] \pstLineAB{B}{O} \pstLineAB{B}{I} \pstLineAB{B}{J} \pstLineAB{B}{K} \pstLineAB{B}{L} \pstLineAB{B}{M} \pstLineAB{B}{M} \pstOrtSym[PointSymbol=none,PointName=none]{A}{B}{I}[I1] \pstOrtSym[PointSymbol=none,PointName=none]{A}{B}{J}[J1] \pstOrtSym[PointSymbol=none,PointName=none]{A}{B}{K}[K1] \pstOrtSym[PointSymbol=none,PointName=none]{A}{B}{L}[L1] \pstOrtSym[PointSymbol=none,PointName=none]{A}{B}{M}[M1] \pstLineAB{O}{M1} \pstLineAB{A}{I1} \pstLineAB{A}{J1} \pstLineAB{A}{K1} \pstLineAB{A}{L1} \pstLineAB{A}{M1} \pstLineAB{B}{I1} \pstLineAB{B}{J1} \pstLineAB{B}{K1} \pstLineAB{B}{L1} \pstLineAB{B}{M1} } \put(2,-2){Figure 2} \endpspicture \end{center} %\begin{comment} \begin{center} \pspicture(-5,-5)(6,2.5) \rput{25}{% \pstGeonode[PointSymbol=none,PointName=none](0,0){O}(1,0){I}(2,0){J}(3,0){K}(4,0){L}(5,0){M}(0,1.4){A} \pstLineAB{A}{O} \pstLineAB{A}{I} \pstLineAB{A}{J} \pstLineAB{A}{K} \pstLineAB{A}{L} \pstLineAB{A}{M} \pstLineAB{O}{M} \pstOrtSym[PointSymbol=none,PointName=none]{O}{M}{A}[B] \pstLineAB{B}{O} \pstLineAB{B}{I} \pstLineAB{B}{J} \pstLineAB{B}{K} \pstLineAB{B}{L} \pstLineAB{B}{M} \pstLineAB{B}{M} \pstOrtSym[PointSymbol=none,PointName=none]{A}{B}{I}[I1] \pstOrtSym[PointSymbol=none,PointName=none]{A}{B}{J}[J1] \pstOrtSym[PointSymbol=none,PointName=none]{A}{B}{K}[K1] \pstOrtSym[PointSymbol=none,PointName=none]{A}{B}{L}[L1] \pstOrtSym[PointSymbol=none,PointName=none]{A}{B}{M}[M1] \pstLineAB{O}{M1} \pstLineAB{A}{I1} \pstLineAB{A}{J1} \pstLineAB{A}{K1} \pstLineAB{A}{L1} \pstLineAB{A}{M1} \pstLineAB{B}{I1} \pstLineAB{B}{J1} \pstLineAB{B}{K1} \pstLineAB{B}{L1} \pstLineAB{B}{M1} \pstSymO[PointSymbol=none,PointName=none]{B}{A}[C] \pstSymO[PointSymbol=none,PointName=none]{B}{I1}[I2] \pstSymO[PointSymbol=none,PointName=none]{B}{J1}[J2] \pstSymO[PointSymbol=none,PointName=none]{B}{K1}[K2] \pstSymO[PointSymbol=none,PointName=none]{B}{L1}[L2] \pstSymO[PointSymbol=none,PointName=none]{B}{M1}[M2] \pstLineAB{B}{C} \pstLineAB{C}{I2} \pstLineAB{C}{J2} \pstLineAB{C}{K2} \pstLineAB{C}{L2} \pstLineAB{C}{M2} \pstLineAB{B}{I2} \pstLineAB{B}{J2} \pstLineAB{B}{K2} \pstLineAB{B}{L2} \pstLineAB{B}{M2} \pstOrtSym[PointSymbol=none,PointName=none]{B}{C}{I2}[I3] \pstOrtSym[PointSymbol=none,PointName=none]{B}{C}{J2}[J3] \pstOrtSym[PointSymbol=none,PointName=none]{B}{C}{K2}[K3] \pstOrtSym[PointSymbol=none,PointName=none]{B}{C}{L2}[L3] \pstOrtSym[PointSymbol=none,PointName=none]{B}{C}{M2}[M3] \pstLineAB{B}{I3} \pstLineAB{B}{J3} \pstLineAB{B}{K3} \pstLineAB{B}{L3} \pstLineAB{B}{M3} \pstLineAB{C}{I3} \pstLineAB{C}{J3} \pstLineAB{C}{K3} \pstLineAB{C}{L3} \pstLineAB{C}{M3} \pstLineAB{M2}{M3} } \put(3,-4){Figure 3} \endpspicture \end{center} {\em Attention à la précision des tracés\ldots} %\end{comment}