%%% % Le th\'eor\`eme de Pythagore %%% \def\filedatePythagore{2025/12/17}% \def\fileversionPythagore{0.1c}% \message{-- \filedatePythagore\space v\fileversionPythagore}% % \setKVdefault[ClesPythagore]{Exact=false,AvantRacine=false,Racine=false,Entier=false,Egalite=false,Precision=2,Soustraction=false,Figure=false,FigureSeule=false,Carres=false,Angle=0,Echelle=1cm,Reciproque=false,ReciColonnes=false,Faible=false,Unite=cm,EnchaineA=false,EnchaineB=false,EnchaineC=false,Perso=false,AllPerso=false,SansMots=false,Decalage=5mm,ModeleCouleur=5,ValeurA={},ValeurB={},ValeurC={},Dys=false,Couleurs={},MyLabel=false,Alias={},UnePart=false}% %\defKV[ClesPythagore]{% %ValeurA=\ifempty{#1}{}{\setKV[ClesPythagore]{EnchaineA}},% %ValeurB=\ifempty{#1}{}{\setKV[ClesPythagore]{EnchaineB}},% % ValeurC=\ifempty{#1}{}{\setKV[ClesPythagore]{EnchaineC}}% %}% \setsepchar[*]{,*/}% \readlist*\ListePythagoreCoteEntier{13/84/85,14/48/50,15/20/25,15/36/39,16/30/34,16/63/65,18/24/30,18/80/82,20/21/29,20/48/52,21/28/35,21/72/75,24/32/40,24/45/51,24/70/74,25/60/65,27/36/45,28/45/53,28/96/100,30/40/50,30/72/78,32/60/68,33/44/55,33/56/65,35/84/91,36/48/60,36/77/85,39/52/65,39/80/89,40/42/58,40/75/85,42/56/70,45/60/75,48/55/73,48/64/80,51/68/85,54/72/90,57/76/95,60/63/87,60/80/100,65/72/97}%%d'après villement.gerard.free.fr%3/4/5}/{5/12/13}/{6/8/10}/{7/24/25}/{8/15/17}/{9/12/15}/{9/40/41}/{10/24/26}/{11/60/61}/{12/16/20}/{12/35/37}/ \setsepchar{,}% % On d\'efinit les figures \`a utiliser \def\MPFigurePytha#1#2#3#4#5#6{% % #1 Premier sommet % #2 Sommet de l'angle droit % #3 troisi\`eme sommet % #4 1ere longueur % #5 2eme longueur % #6 angle de rotation de la figure \mplibforcehmode% \begin{mplibcode} defaultcolormodel := \useKV[ClesPythagore]{ModeleCouleur}; boolean Dys,Carres,MyLabel; Dys=\useKV[ClesPythagore]{Dys}; Carres=\useKV[ClesPythagore]{Carres}; MyLabel=\useKV[ClesPythagore]{MyLabel}; % \ifemptyKV[ClesPythagore]{Couleurs}{}{% nb:=0; color CoulCote[]; for p_=\useKV[ClesPythagore]{Couleurs}: nb:=nb+1; CoulCote[nb]=p_; endfor; }% u:=\useKV[ClesPythagore]{Echelle}; pair A,B,C,O,D,E,F;%B est le sommet de l'angle droit O=u*(2.5,2.5); path cc; cc=(fullcircle scaled 4u) shifted O; % On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure A=point(0.9*length cc) of cc; B=A rotatedabout(O,-120); C=2[A,O]; % On tourne pour \'eventuellement moins de lassitude :) A:=A rotatedabout(O,#6); B:=B rotatedabout(O,#6); C:=C rotatedabout(O,#6); % On d\'efinit l'angle droit D-B=7*unitvector(C-B); F-B=7*unitvector(A-B); E-D=F-B; if Carres: drawoptions(dashed evenly); pair M[],N[],P[]; M1=rotation(A,B,-90); M2=rotation(B,A,90); if known CoulCote[2]: fill polygone(A,B,M1,M2) withcolor CoulCote[2]; fi; draw B{dir(angle(M1-B)+5)}..{dir(angle(M1-B)+5)}M1{dir(angle(M2-M1)+5)}..{dir(angle(M2-M1)+5)}M2{dir(angle(A-M2)+5)}..{dir(angle(A-M2)+5)}A; N1=rotation(C,B,90); N2=rotation(B,C,-90); if known CoulCote[1]: fill polygone(C,B,N1,N2) withcolor CoulCote[1]; fi; draw B{dir(angle(N1-B)+5)}..{dir(angle(N1-B)+5)}N1{dir(angle(N2-N1)+5)}..{dir(angle(N2-N1)+5)}N2{dir(angle(C-N2)+5)}..{dir(angle(C-N2)+5)}C; P1=rotation(C,A,-90); P2=rotation(A,C,90); if known CoulCote[3]: fill polygone(C,A,P1,P2) withcolor CoulCote[3]; fi; draw A{dir(angle(P1-A)+5)}..{dir(angle(P1-A)+5)}P1{dir(angle(P2-P1)+5)}..{dir(angle(P2-P1)+5)}P2{dir(angle(C-P2)+5)}..{dir(angle(C-P2)+5)}C; drawoptions(); fi; draw A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)} if known CoulCote[2]:withcolor CoulCote[2] fi; draw B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)} if known CoulCote[1]:withcolor CoulCote[1] fi; draw C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)} if known CoulCote[3]:withcolor CoulCote[3] fi; draw D--E--F; numeric decalage; if Dys: decalage=2*\useKV[ClesPythagore]{Decalage}; labeloffset:=labeloffset*2; else: decalage=\useKV[ClesPythagore]{Decalage}; labeloffset:=labeloffset*1.5; fi; if MyLabel : if (#4<#5) or (#4=#5) : Mylabel(TEX("\num{#4}"),C--B,0.5); Mylabel(TEX("\num{#5}"),B--A,0.5); else: Mylabel(TEX("\num{#4}"),A--C,0.5); Mylabel(TEX("\num{#5}"),B--A,0.5); fi; else: if (#4<#5) or (#4=#5) : if ypart(B)>ypart(O) : label(btex \num{#4} etex,1/2[C,B]-decalage*(unitvector(A-B))); label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); else: label(btex \num{#4} etex,1/2[C,B]-decalage*(unitvector(A-B))); label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); fi else: if ypart(B)>ypart(O) : label(btex \num{#4} etex,1/2[C,A]-decalage*(unitvector(C-A) rotated 90)); label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); else: label(btex \num{#4} etex,1/2[A,C]+decalage*(unitvector(A-C) rotated 90)); label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); fi; fi; fi; pair I; I=CentreCercleI(A,B,C); Labelcp(I)(TEX("#1"),C); Labelcp(I)(TEX("#2"),B); Labelcp(I)(TEX("#3"),A); \end{mplibcode} }% \def\MPFigureReciPytha#1#2#3#4#5#6#7{% % #1 Premier sommet % #2 Sommet de l'angle droit % #3 troisi\`eme sommet % #4 1ere longueur % #5 2eme longueur % #6 3eme longueur % #7 angle de rotation de la figure \mplibforcehmode \begin{mplibcode} defaultcolormodel := \useKV[ClesPythagore]{ModeleCouleur}; u:=\useKV[ClesPythagore]{Echelle}; boolean Dys; Dys=\useKV[ClesPythagore]{Dys}; decalage=if Dys:2* fi \useKV[ClesPythagore]{Decalage}; pair A,B,C,O,D,E,F;%B est le sommet de l'angle droit O=u*(2.5,2.5); path cc; cc=(fullcircle scaled 4u) shifted O; % On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure A=point(0.8*length cc) of cc; B=A rotatedabout(O,-100); C=2[A,O]; % On tourne pour \'eventuellement moins de lassitude :) A:=A rotatedabout(O,#7); B:=B rotatedabout(O,#7); C:=C rotatedabout(O,#7); draw A{dir(angle(B-A)+5)}..B{dir(angle(B-A)+5)}; draw B{dir(angle(C-B)+5)}..C{dir(angle(C-B)+5)}; draw C{dir(angle(A-C)+5)}..A{dir(angle(A-C)+5)}; label(TEX("\num{#4}"),O+decalage*(unitvector(O-B))); label(TEX("\num{#6}"),1/2[C,B]+decalage*(unitvector(1/2[C,B]-O))); label(TEX("\num{#5}"),1/2[A,B]+decalage*(unitvector(1/2[A,B]-O))); label(TEX("#1"),1.2[O,A]); label(TEX("#2"),1.2[O,B]); label(TEX("#3"),1.2[O,C]); \end{mplibcode} }% \def\MPFigurePythaSansMots#1#2#3#4#5#6{% % #1 Premier sommet % #2 Sommet de l'angle droit % #3 troisi\`eme sommet % #4 1ere longueur % #5 2eme longueur % #6 angle de rotation de la figure \mplibforcehmode \begin{mplibcode} defaultcolormodel := \useKV[ClesPythagore]{ModeleCouleur}; u:=\useKV[ClesPythagore]{Echelle}; boolean Dys; Dys=\useKV[ClesPythagore]{Dys}; numeric decalage; decalage=if Dys:2* fi \useKV[ClesPythagore]{Decalage}; pair A,B,C,O,D,E,F,L[],M[],N[];%B est le sommet de l'angle droit O=u*(2.5,2.5); path cc; cc=(fullcircle scaled 4u) shifted O; % On place les points A,B,C sur le cercle de mani\`ere \`a faciliter la rotation de la figure A=point(0.9*length cc) of cc; B=A rotatedabout(O,-120); C=2[A,O]; % On tourne pour \'eventuellement moins de lassitude :) A:=A rotatedabout(O,#6); B:=B rotatedabout(O,#6); C:=C rotatedabout(O,#6); % On d\'efinit l'angle droit D-B=7*unitvector(C-B); F-B=7*unitvector(A-B); E-D=F-B; trace polygone(A,B,C); draw D--E--F; L1=rotation(B,A,90); L2-L1=B-A; trace chemin(A,L1,L2,B); M1=rotation(C,B,90); M2-M1=C-B; trace chemin(B,M1,M2,C); N1=rotation(A,C,90); N2-N1=A-C; trace chemin(C,N1,N2,A); if (#4<#5) or (#4=#5) : if ypart(B)>ypart(O) : label(btex \num{#4} etex,1/2[C,B]+decalage*(unitvector(A-B))); label(btex \num{#5} etex,1/2[A,B]+decalage*(unitvector(C-B))); label(TEX("\begin{tabular}{c}Aire\\$\num{#5}\times\num{#5}$\\$\num{\fpeval{#5*#5}}$\\\end{tabular}"),iso(A,L2)); label(TEX("\begin{tabular}{c}Aire\\$\num{#4}\times\num{#4}$\\$\num{\fpeval{#4*#4}}$\\\end{tabular}"),iso(B,M2)); label(TEX("\begin{tabular}{c}Aire\\$\num{\fpeval{#4*#4}}+\num{\fpeval{#5*#5}}$\\$\num{\fpeval{#4*#4+#5*#5}}$\\\end{tabular}"),iso(C,N2)); else: label(btex \num{#4} etex,1/2[C,B]+decalage*(unitvector(A-B))); label(btex \num{#5} etex,1/2[A,B]+decalage*(unitvector(C-B))); label(TEX("\begin{tabular}{c}Aire\\$\num{#5}\times\num{#5}$\\$\num{\fpeval{#5*#5}}$\\\end{tabular}"),iso(A,L2)); label(TEX("\begin{tabular}{c}Aire\\$\num{#4}\times\num{#4}$\\$\num{\fpeval{#4*#4}}$\\\end{tabular}"),iso(B,M2)); label(TEX("\begin{tabular}{c}Aire\\$\num{\fpeval{#4*#4}}+\num{\fpeval{#5*#5}}$\\$\num{\fpeval{#4*#4+#5*#5}}$\\\end{tabular}"),iso(C,N2)); drawarrow 2/10[iso(A,L2),iso(C,N2)]--8/10[iso(A,L2),iso(C,N2)]; drawarrow 2/10[iso(B,M2),iso(C,N2)]--8/10[iso(B,M2),iso(C,N2)]; fi else: if ypart(B)>ypart(O) : label(btex \num{#4} etex,1/2[C,A]-decalage*(unitvector(C-A) rotated 90)); label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); label(TEX("\begin{tabular}{c}Aire\\$\num{#5}\times\num{#5}$\\$\num{\fpeval{#5*#5}}$\\\end{tabular}"),iso(A,L2)); label(TEX("\begin{tabular}{c}Aire\\$\num{#4}\times\num{#4}$\\$\num{\fpeval{#4*#4}}$\\\end{tabular}"),iso(C,N2)); label(TEX("\begin{tabular}{c}Aire\\$\num{\fpeval{#4*#4}}-\num{\fpeval{#5*#5}}$\\$\num{\fpeval{#4*#4-#5*#5}}$\\\end{tabular}"),iso(B,M2)); drawarrow 2/10[iso(A,L2),iso(B,M2)]--8/10[iso(A,L2),iso(B,M2)]; drawarrow 2/10[iso(C,N2),iso(B,M2)]--8/10[iso(C,N2),iso(B,M2)]; else: label(btex \num{#4} etex,1/2[A,C]+decalage*(unitvector(A-C) rotated 90)); label(btex \num{#5} etex,1/2[A,B]-decalage*(unitvector(C-B))); label(TEX("\begin{tabular}{c}Aire\\$\num{#5}\times\num{#5}$\\$\num{\fpeval{#5*#5}}$\\\end{tabular}"),iso(A,L2)); label(TEX("\begin{tabular}{c}Aire\\$\num{#4}\times\num{#4}$\\$\num{\fpeval{#4*#4}}$\\\end{tabular}"),iso(C,N2)); label(TEX("\begin{tabular}{c}Aire\\$\num{\fpeval{#4*#4}}-\num{\fpeval{#5*#5}}$\\$\num{\fpeval{#4*#4-#5*#5}}$\\\end{tabular}"),iso(B,M2)); drawarrow 2/10[iso(A,L2),iso(B,M2)]--8/10[iso(A,L2),iso(B,M2)]; drawarrow 2/10[iso(C,N2),iso(B,M2)]--8/10[iso(C,N2),iso(B,M2)]; fi; fi; label(btex #3 etex,1.2[O,A]); label(btex #2 etex,1.2[O,B]); label(btex #1 etex,1.2[O,C]); \end{mplibcode} }% \newcommand\RedactionPythagore{}% \newcommand\RedactionReciPythagore{}% \newcommand\RedactionCalculsPythagore{}% \newcommand\RedactionCalculsReciPythagore{}% \newcommand\RedactionConclusionReciPythagore{}% \NewDocumentCommand\CalculsPythagore{o m m m m}{% \ifemptyKV[ClesPythagore]{Couleurs}{\setsepchar{,}\ignoreemptyitems\readlist*\PfCListeCouleursPytha{black,black,black}\reademptyitems}{\edef\PfCListeCouleursAv{\useKV[ClesPythagore]{Couleurs}}\setsepchar{,}\ignoreemptyitems\readlist*\PfCListeCouleursPytha{\PfCListeCouleursAv}\reademptyitems}% \ifnum\PfCListeCouleursPythalen<3\relax% \edef\PfCListeCouleursAv{\useKV[ClesPythagore]{Couleurs}}% \xintFor* ##1 in{\xintSeq{1}{\fpeval{3-\PfCListeCouleursPythalen}}}\do{% \edef\PfCListeCouleursAv{\PfCListeCouleursAv,black}% }% \setsepchar{,}\ignoreemptyitems% \readlist*\PfCListeCouleursPytha{\PfCListeCouleursAv}% \reademptyitems% \fi% \ifemptyKV[ClesPythagore]{Alias}{% \edef\PfCPythaNomHypo{\NomA\NomC}% \edef\PfCPythaNomPremierCote{\NomA\NomB}% \edef\PfCPythaNomDeuxiemeCote{\NomB\NomC}% }{% \setsepchar{,}\ignoreemptyitems% \edef\PfCFooAlias{\useKV[ClesPythagore]{Alias}}% \readlist*\PfCListeAliasCotes{\PfCFooAlias}% \reademptyitems% \edef\PfCPythaNomHypo{\PfCListeAliasCotes[1]}% \edef\PfCPythaNomPremierCote{\PfCListeAliasCotes[2]}% \edef\PfCPythaNomDeuxiemeCote{\PfCListeAliasCotes[3]}% } \xintifboolexpr{#3<#4 || #3==#4}{%\ifnum#3<#4% \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2+#4^2),\useKV[ClesPythagore]{Precision})}}% \ifemptyKV[ClesPythagore]{ValeurA}{\xdef\PfCPythaVA{\fpeval{#3^2}}}{\setKV[ClesPythagore]{EnchaineA}\xdef\PfCPythaVA{\useKV[ClesPythagore]{ValeurA}}}% \ifemptyKV[ClesPythagore]{ValeurB}{\xdef\PfCPythaVB{\fpeval{#4^2}}}{\setKV[ClesPythagore]{EnchaineB}\xdef\PfCPythaVB{\useKV[ClesPythagore]{ValeurB}}}% \xdef\ResultatAttendu{\fpeval{\PfCPythaVA+\PfCPythaVB}}% \xdef\ResultatApproche{\fpeval{round(sqrt(\ResultatAttendu),\useKV[ClesPythagore]{Precision})^2}}% \begin{align*} \mathcolor{\PfCListeCouleursPytha[3]}{\PfCPythaNomHypo}^2&=\mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}^2+\mathcolor{\PfCListeCouleursPytha[2]}{\PfCPythaNomDeuxiemeCote}^2\\ \mathcolor{\PfCListeCouleursPytha[3]}{\PfCPythaNomHypo}^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opcopy{\useKV[ClesPythagore]{ValeurA}}{a1}\opexport{a1}{\Aun}\mathcolor{\PfCListeCouleursPytha[1]}{\num{\Aun}}}{\opexport{A1}{\Aun}\mathcolor{\PfCListeCouleursPytha[1]}{\num{\Aun}}^2}+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}}{\opexport{A2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}^2}\\ \mathcolor{\PfCListeCouleursPytha[3]}{\PfCPythaNomHypo}^2&=\ifboolKV[ClesPythagore]{EnchaineA}{\opexport{a1}{\Aun}\num{\Aun}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\mathcolor{\PfCListeCouleursPytha[1]}{\num{\Aun}}}+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}}\\ \mathcolor{\PfCListeCouleursPytha[3]}{\PfCPythaNomHypo}^2&=\opadd*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\ \ifboolKV[ClesPythagore]{AvantRacine}{}{% \ifboolKV[ClesPythagore]{Entier}{}{\\\mathcolor{\PfCListeCouleursPytha[3]}{\PfCPythaNomHypo}&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}\ifboolKV[ClesPythagore]{Racine}{~\si{\PfCPythaUnit}}{}} \ifboolKV[ClesPythagore]{Racine}{}{\\\mathcolor{\PfCListeCouleursPytha[3]}{\PfCPythaNomHypo}&\IfStrEq{\ResultatApproche}{\ResultatAttendu}{=}{\approx}\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}%\\ } \end{align*} }{% \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2-#4^2),\useKV[ClesPythagore]{Precision})}}% \ifemptyKV[ClesPythagore]{ValeurC}{\xdef\PfCPythaVC{\fpeval{#3^2}}}{\setKV[ClesPythagore]{EnchaineC}\xdef\PfCPythaVC{\useKV[ClesPythagore]{ValeurC}}}% \ifemptyKV[ClesPythagore]{ValeurB}{\xdef\PfCPythaVB{\fpeval{#4^2}}}{\setKV[ClesPythagore]{EnchaineB}\xdef\PfCPythaVB{\useKV[ClesPythagore]{ValeurB}}}% \xdef\ResultatAttendu{\fpeval{\PfCPythaVC-\PfCPythaVB}}% \xdef\ResultatApproche{\fpeval{round(sqrt(\ResultatAttendu),\useKV[ClesPythagore]{Precision})^2}}% \ifboolKV[ClesPythagore]{Soustraction}{% \begin{align*} \mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}^2&=\mathcolor{\PfCListeCouleursPytha[3]}{\PfCPythaNomHypo}^2-\mathcolor{\PfCListeCouleursPytha[2]}{\PfCPythaNomDeuxiemeCote}^2\\ \mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\mathcolor{\PfCListeCouleursPytha[3]}{\num{\Aun}}}{\opexport{A1}{\Aun}\mathcolor{\PfCListeCouleursPytha[3]}{\num{\Aun}}^2}-\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}}{\opexport{A2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}^2}\\ \mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\mathcolor{\PfCListeCouleursPytha[3]}{\num{\Aun}}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\mathcolor{\PfCListeCouleursPytha[3]}{\num{\Aun}}}-\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}}\\ \mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}^2&=\opsub*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\ \ifboolKV[ClesPythagore]{AvantRacine}{}{% \ifboolKV[ClesPythagore]{Entier}{}{\\\mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}\ifboolKV[ClesPythagore]{Racine}{~\si{\PfCPythaUnit}}{}} \ifboolKV[ClesPythagore]{Racine}{}{\\\mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}&\IfStrEq{\ResultatApproche}{\ResultatAttendu}{=}{\approx}\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}%\\ } \end{align*} }{% \begin{align*} \mathcolor{\PfCListeCouleursPytha[3]}{\PfCPythaNomHypo}^2&=\mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}^2+\mathcolor{\PfCListeCouleursPytha[2]}{\PfCPythaNomDeuxiemeCote}^2\\ \ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\mathcolor{\PfCListeCouleursPytha[3]}{\num{\Aun}}}{\opexport{A1}{\Aun}\mathcolor{\PfCListeCouleursPytha[3]}{\num{\Aun}}^2}&=\mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}^2+\ifboolKV[ClesPythagore]{EnchaineB}{\opcopy{\useKV[ClesPythagore]{ValeurB}}{a2}\opexport{a2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}}{\opexport{A2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}^2}\\ \ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\mathcolor{\PfCListeCouleursPytha[3]}{\num{\Aun}}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\mathcolor{\PfCListeCouleursPytha[3]}{\num{\Aun}}}&=\mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}^2+\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[3]}{\num{\Adeux}}}\\ \mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}^2&=\ifboolKV[ClesPythagore]{EnchaineC}{\opcopy{\useKV[ClesPythagore]{ValeurC}}{a1}\opexport{a1}{\Aun}\mathcolor{\PfCListeCouleursPytha[3]}{\num{\Aun}}}{\opmul*{A1}{A1}{a1}\opexport{a1}{\Aun}\mathcolor{\PfCListeCouleursPytha[3]}{\num{\Aun}}}-\ifboolKV[ClesPythagore]{EnchaineB}{\opexport{a2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}}{\opmul*{A2}{A2}{a2}\opexport{a2}{\Adeux}\mathcolor{\PfCListeCouleursPytha[2]}{\num{\Adeux}}}\\ \mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}^2&=\opsub*{a1}{a2}{a3}\opexport{a3}{\Atrois}\num{\Atrois}%\\ \ifboolKV[ClesPythagore]{AvantRacine}{}{% \ifboolKV[ClesPythagore]{Entier}{}{\\\mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}&=\sqrt{\opexport{a3}{\Atrois}\num{\Atrois}}\ifboolKV[ClesPythagore]{Racine}{~\si{\PfCPythaUnit}}{}}% \ifboolKV[ClesPythagore]{Racine}{}{\\\mathcolor{\PfCListeCouleursPytha[1]}{\PfCPythaNomPremierCote}&\IfStrEq{\ResultatApproche}{\ResultatAttendu}{=}{\approx}\opsqrt[maxdivstep=5]{a3}{a4}\opround{a4}{pres}{a4}\opunzero{a4}\opexport{a4}{\Aquatre}\SI{\Aquatre}{\PfCPythaUnit}}%\\ } \end{align*} }% }% }% \NewDocumentCommand\PfCCalculsReciPythagore{ommmm}{% \ifboolKV[ClesPythagore]{UnePart}{% \par% \ifPfCDeuxColonnes% \else% \begin{minipage}[t]{0.45\linewidth}% \fi D'une part : \begin{align*} &\NomA\NomC^2\\ &\ifboolKV[ClesPythagore]{EnchaineC}{% \num{\useKV[ClesPythagore]{ValeurC}}% \xdef\PfCRetiensReciHypo{\useKV[ClesPythagore]{ValeurC}}% }{% \num{#3}^2}\\ &\ifboolKV[ClesPythagore]{EnchaineC}{}{% \xdef\PfCRetiensReciHypo{\fpeval{#3*#3}}% \num{\PfCRetiensReciHypo} } \end{align*} \ifPfCDeuxColonnes% \else% \end{minipage}\hfill \begin{minipage}[t]{0.45\linewidth} \fi% D'autre part : \begin{align*} &\NomA\NomB^2+\NomB\NomC^2\\ &\ifboolKV[ClesPythagore]{EnchaineA}{\num{\useKV[ClesPythagore]{ValeurA}}}{\num{#4}^2}+\ifboolKV[ClesPythagore]{EnchaineB}{\num{\useKV[ClesPythagore]{ValeurB}}}{\num{#5}^2}\\ &\ifboolKV[ClesPythagore]{EnchaineA}{%Enchaine A \ifboolKV[ClesPythagore]{EnchaineB}{%EnchaineB }{%Pas Enchaine B \num{\useKV[ClesPythagore]{ValeurA}}}}{%Pas EnchaineA \num{\fpeval{#4*#4}}}\ifboolKV[ClesPythagore]{EnchaineA}{\ifboolKV[ClesPythagore]{EnchaineB}{}{+}}{+}\ifboolKV[ClesPythagore]{EnchaineB}{%Enchaine B \ifboolKV[ClesPythagore]{EnchaineA}{%EnchaineA }{%Pas Enchaine A \num{\useKV[ClesPythagore]{ValeurB}}}}{%Pas EnchaineB \num{\fpeval{#5*#5}}}\\ &\ifboolKV[ClesPythagore]{EnchaineA}{%Enchaine A \ifboolKV[ClesPythagore]{EnchaineB}{%EnchaineB \xdef\PfCRetiensReciSomme{\fpeval{\useKV[ClesPythagore]{ValeurA}+\useKV[ClesPythagore]{ValeurB}}}% }{%Pas Enchaine B \xdef\PfCRetiensReciSomme{\fpeval{\useKV[ClesPythagore]{ValeurA}+#5*#5}}% }}{%Pas EnchaineA \ifboolKV[ClesPythagore]{EnchaineB}{ \xdef\PfCRetiensReciSomme{\fpeval{\useKV[ClesPythagore]{ValeurB}+#4*#4}}% }{% \xdef\PfCRetiensReciSomme{\fpeval{#4*#4+#5*#5}}% } } \num{\PfCRetiensReciSomme}% \end{align*} \ifPfCDeuxColonnes% \else% \end{minipage}\par \fi% }{% \ifboolKV[ClesPythagore]{ReciColonnes}{% \[ \begin{array}{cccc|cccc}% &&\NomA\NomC^2&&&\NomA\NomB^2&+&\NomB\NomC^2\\ &&\ifboolKV[ClesPythagore]{EnchaineC}{% \num{\useKV[ClesPythagore]{ValeurC}}% \xdef\PfCRetiensReciHypo{\useKV[ClesPythagore]{ValeurC}}% }{% \num{#3}^2}&&&\ifboolKV[ClesPythagore]{EnchaineA}{\num{\useKV[ClesPythagore]{ValeurA}}}{\num{#4}^2}&+&\ifboolKV[ClesPythagore]{EnchaineB}{\num{\useKV[ClesPythagore]{ValeurB}}}{\num{#5}^2}\\ &&&&&\ifboolKV[ClesPythagore]{EnchaineA}{%Enchaine A \ifboolKV[ClesPythagore]{EnchaineB}{%EnchaineB }{%Pas Enchaine B \num{\useKV[ClesPythagore]{ValeurA}}}}{%Pas EnchaineA \num{\fpeval{#4*#4}}}&\ifboolKV[ClesPythagore]{EnchaineA}{\ifboolKV[ClesPythagore]{EnchaineB}{}{+}}{+}&\ifboolKV[ClesPythagore]{EnchaineB}{%Enchaine B \ifboolKV[ClesPythagore]{EnchaineA}{%EnchaineA }{%Pas Enchaine A \num{\useKV[ClesPythagore]{ValeurB}}}}{%Pas EnchaineB \num{\fpeval{#5*#5}}}\\ &&\ifboolKV[ClesPythagore]{EnchaineC}{}{% \xdef\PfCRetiensReciHypo{\fpeval{#3*#3}}% \num{\PfCRetiensReciHypo} }&&&\multicolumn{3}{c}{% \ifboolKV[ClesPythagore]{EnchaineA}{%Enchaine A \ifboolKV[ClesPythagore]{EnchaineB}{%EnchaineB \xdef\PfCRetiensReciSomme{\fpeval{\useKV[ClesPythagore]{ValeurA}+\useKV[ClesPythagore]{ValeurB}}}% }{%Pas Enchaine B \xdef\PfCRetiensReciSomme{\fpeval{\useKV[ClesPythagore]{ValeurA}+#5*#5}}% }}{%Pas EnchaineA \ifboolKV[ClesPythagore]{EnchaineB}{ \xdef\PfCRetiensReciSomme{\fpeval{\useKV[ClesPythagore]{ValeurB}+#4*#4}}% }{% \xdef\PfCRetiensReciSomme{\fpeval{#4*#4+#5*#5}}% } } \num{\PfCRetiensReciSomme}% }\\ \end{array} \] }{% \[\left. \begin{array}{l} \NomA\NomC^2=\ifboolKV[ClesPythagore]{EnchaineC}{% \num{\useKV[ClesPythagore]{ValeurC}}% \xdef\PfCRetiensReciHypo{\useKV[ClesPythagore]{ValeurC}}% }{% \num{#3}^2=\num{\fpeval{#3*#3}} \xdef\PfCRetiensReciHypo{\fpeval{#3*#3}}% }\\ \NomA\NomB^2+\NomB\NomC^2=\ifboolKV[ClesPythagore]{EnchaineA}{\num{\useKV[ClesPythagore]{ValeurA}}}{\num{#4}^2}+\ifboolKV[ClesPythagore]{EnchaineB}{\num{\useKV[ClesPythagore]{ValeurB}}}{\num{#5}^2}= \ifboolKV[ClesPythagore]{EnchaineA}{%Enchaine A \ifboolKV[ClesPythagore]{EnchaineB}{%Enchaine B \xdef\PfCRetiensReciSomme{\fpeval{\useKV[ClesPythagore]{ValeurA}+\useKV[ClesPythagore]{ValeurB}}}% \num{\PfCRetiensReciSomme}% }{% PasEnchaine B \num{\useKV[ClesPythagore]{ValeurA}}+\num{\fpeval{#5*#5}}=% \xdef\PfCRetiensReciSomme{\fpeval{\useKV[ClesPythagore]{ValeurA}+#5*#5}}% \num{\PfCRetiensReciSomme}% } }{%Pas Enchaine A \num{\fpeval{#4*#4}}+ \ifboolKV[ClesPythagore]{EnchaineB}{%Enchaine B \num{\useKV[ClesPythagore]{ValeurB}}=\xdef\PfCRetiensReciSomme{\fpeval{\useKV[ClesPythagore]{ValeurB}+#4*#4}}% \num{\PfCRetiensReciSomme}% }{%Pas Enchaine B \num{\fpeval{#5*#5}}=\xdef\PfCRetiensReciSomme{\fpeval{#5*#5+#4*#4}}% \num{\PfCRetiensReciSomme}% } } \end{array} \right\}\xintifboolexpr{\PfCRetiensReciHypo==\PfCRetiensReciSomme}{\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2}{\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2}% \] }% }% }% \makeatletter \NewDocumentCommand\NPythagore{om}{% \useKVdefault[ClesPythagore]% \setKV[ClesPythagore]{#1}% \PfC@Pythagore@i#2,% \ifnum\PfC@NumHypo>0\relax% \edef\PfCAroValeurA{\PfC@ValeurA}% \edef\PfCAroValeurB{\PfC@ValeurB}% \ifnum\fpeval{\PfC@NbPointInterA+\PfC@NbPointInterB+\PfC@NbPointInterC}=0\relax% \edef\PfCAroValeurC{\PfC@ValeurC}% \Pythagore[#1,Reciproque]{\NomTriangle}{\PfCAroValeurA}{\PfCAroValeurC}{\PfCAroValeurB}% \else% \Pythagore[#1]{\NomTriangle}{\PfCAroValeurA}{\PfCAroValeurB}{}% \fi% \fi% }% \def\PfC@Pythagore@i#1#2=#3,#4#5=#6,#7#8=#9,{% % On récupère les infos \edef\PfC@NumHypo{0}% \IfEndWith{#1#2}{*}{% \edef\PfC@NumHypo{1}% \StrCut{#1#2}{*}\PfC@Hypo\csAa% }{}% \IfEndWith{#4#5}{*}{% \edef\PfC@NumHypo{2}% \StrCut{#4#5}{*}\PfC@Hypo\csAa% }{}% \IfEndWith{#7#8}{*}{% \edef\PfC@NumHypo{3}% \StrCut{#7#8}{*}\PfC@Hypo\csAa% }{}% \ifnum\PfC@NumHypo=0\relax L'«hypoténuse » n'est pas définie. \else \edef\PfC@CsA{#3}% \edef\PfC@CsB{#6}% \edef\PfC@CsC{#9}% \StrCount{#3}{?}[\PfC@NbPointInterA]% \StrCount{#6}{?}[\PfC@NbPointInterB]% \StrCount{#9}{?}[\PfC@NbPointInterC]% \StrMid{\PfC@Hypo}{1}{1}[\PfC@Tutu]% \StrMid{\PfC@Hypo}{2}{2}[\PfC@Tata]% \edef\PfC@Titi{#1#2#4#5#7#8}% \StrDel{\PfC@Titi}{*}[\PfC@SupportTriangle]% \StrDel{\PfC@SupportTriangle}{\PfC@Tutu}[\PfC@SupportTriangle]% \StrDel{\PfC@SupportTriangle}{\PfC@Tata}[\PfC@SupportTriangle]% \StrMid{\PfC@SupportTriangle}{1}{1}[\NomAngleDroit]% \ifnum\fpeval{\PfC@NbPointInterA+\PfC@NbPointInterB+\PfC@NbPointInterC}=0\relax% \Rangement[Seul]{#3,#6,#9}% \setsepchar{,}\ignoreemptyitems% \readlist*\PfC@ListeValeurReci{\PfCRetiensRangement}% \reademptyitems% \edef\PfC@ValeurA{\PfC@ListeValeurReci[3]}% \edef\PfC@ValeurB{\PfC@ListeValeurReci[2]}% \edef\PfC@ValeurC{\PfC@ListeValeurReci[1]}% \IfStrEqCase{\PfC@NumHypo}{% {3}{\xintifboolexpr{#3>#6}{% \StrDel{#4#5}{\NomAngleDroit}[\PfC@SommetCherche]% }{% \StrDel{#1#2}{\NomAngleDroit}[\PfC@SommetCherche]% }% }% {2}{\xintifboolexpr{#3>#9}{% \StrDel{#7#8}{\NomAngleDroit}[\PfC@SommetCherche]% }{% \StrDel{#1#2}{\NomAngleDroit}[\PfC@SommetCherche]% }% }% {1}{\xintifboolexpr{#6>#9}{% \StrDel{#7#8}{\NomAngleDroit}[\PfC@SommetCherche]% }{% \StrDel{#4#5}{\NomAngleDroit}[\PfC@SommetCherche]% }% }% }% \StrDel{\PfC@Hypo}{\PfC@SommetCherche}[\PfC@SommetNonCherche]% \edef\NomTriangle{\PfC@SommetCherche\NomAngleDroit\PfC@SommetNonCherche}% \else% \IfStrEq{\PfC@CsA}{?}{% \ifnum\PfC@NumHypo=1\relax% \xintifboolexpr{\PfC@CsC>\PfC@CsB}{% \StrDel{#4#5}{\NomAngleDroit}[\PfC@SommetCherche]% }{% \StrDel{#7#8}{\NomAngleDroit}[\PfC@SommetCherche]% }% \edef\PfC@ValeurA{\fpeval{min(\PfC@CsC,\PfC@CsB)}}% \edef\PfC@ValeurB{\fpeval{max(\PfC@CsC,\PfC@CsB)}}% \else% \StrDel{#1#2}{\NomAngleDroit}[\PfC@SommetCherche]% \edef\PfC@ValeurA{\fpeval{max(\PfC@CsC,\PfC@CsB)}}% \edef\PfC@ValeurB{\fpeval{min(\PfC@CsC,\PfC@CsB)}}% \fi% }{% \IfStrEq{\PfC@CsB}{?}{% \ifnum\PfC@NumHypo=2\relax% \xintifboolexpr{\PfC@CsC>\PfC@CsA}{% \StrDel{#1#2}{\NomAngleDroit}[\PfC@SommetCherche]% }{% \StrDel{#7#8}{\NomAngleDroit}[\PfC@SommetCherche]% }% \edef\PfC@ValeurA{\fpeval{min(\PfC@CsC,\PfC@CsA)}}% \edef\PfC@ValeurB{\fpeval{max(\PfC@CsC,\PfC@CsA)}}% \else% \StrDel{#4#5}{\NomAngleDroit}[\PfC@SommetCherche]% \edef\PfC@ValeurA{\fpeval{max(\PfC@CsC,\PfC@CsA)}}% \edef\PfC@ValeurB{\fpeval{min(\PfC@CsC,\PfC@CsA)}}% \fi% }{% \ifnum\PfC@NumHypo=3\relax% \xintifboolexpr{\PfC@CsB>\PfC@CsA}{% \StrDel{#1#2}{\NomAngleDroit}[\PfC@SommetCherche]% }{% \StrDel{#4#5}{\NomAngleDroit}[\PfC@SommetCherche]% }% \edef\PfC@ValeurA{\fpeval{min(\PfC@CsB,\PfC@CsA)}}% \edef\PfC@ValeurB{\fpeval{max(\PfC@CsB,\PfC@CsA)}}% \else% \StrDel{#7#8}{\NomAngleDroit}[\PfC@SommetCherche]% \edef\PfC@ValeurA{\fpeval{max(\PfC@CsB,\PfC@CsA)}}% \edef\PfC@ValeurB{\fpeval{min(\PfC@CsB,\PfC@CsA)}}% \fi% }% }% \StrDel{\PfC@Hypo}{\PfC@SommetCherche}[\PfC@SommetNonCherche]% \edef\NomTriangle{\PfC@SommetCherche\NomAngleDroit\PfC@SommetNonCherche}% \fi% \fi }% \makeatother \NewDocumentCommand\Pythagore{o m m m m}{% % #1 Param\`etres sous forme de cl\'es % #2 Nom "complet" du triangle : ABC par exemple % #3 Premi\`ere longueur % #4 Deuxi\`eme longueur % #5 Troisi\`eme longueur (\'eventuellement vide) \useKVdefault[ClesPythagore]% \setKV[ClesPythagore]{#1}% \ifPfCPfMScratchDys\relax\setKV[ClesPythagore]{Dys}\fi% \DeclareSIUnit{\PfCPythaUnit}{\useKV[ClesPythagore]{Unite}}% \ifboolKV[ClesPythagore]{Reciproque}{% % On retient les noms des sommets \StrMid{#2}{1}{1}[\NomA]% \StrMid{#2}{2}{2}[\NomB]% \StrMid{#2}{3}{3}[\NomC]% \xdef\NomTriangle{\NomA\NomB\NomC}% % on stocke les valeurs donn\'ees \opcopy{#3}{A1}% \opcopy{#4}{A2}% \opcopy{#5}{A3}% \xdef\GrandCote{#3}% \xdef\PetitCote{#4}% \xdef\MoyenCote{#5}% % On trace une figure ou pas ? \ifboolKV[ClesPythagore]{FigureSeule}{% \MPFigureReciPytha{\NomA}{\NomB}{\NomC}{#3}{#4}{#5}{\useKV[ClesPythagore]{Angle}}% }{% \ifboolKV[ClesPythagore]{Figure}{%Utilisation obligatoire de l'option --shell-escape de la compilation \begin{multicols}{2} {\em La figure est donn\'ee \`a titre indicatif.}% \[\MPFigureReciPytha{\NomA}{\NomB}{\NomC}{#3}{#4}{#5}{\useKV[ClesPythagore]{Angle}}\]% \par\columnbreak\par% \ifboolKV[ClesPythagore]{AllPerso}{% \RedactionReciPythagore% \RedactionCalculsReciPythagore% \RedactionConclusionReciPythagore% }{% % on r\'edige \ifboolKV[ClesPythagore]{Perso}{% \RedactionReciPythagore% }{% Dans le triangle $#2$, $[\NomA\NomC]$ est le plus grand c\^ot\'e.% }% \PfCCalculsReciPythagore[#1]{#2}{#3}{#4}{#5}% \ifboolKV[ClesPythagore]{Egalite}{% \xintifboolexpr{\PfCRetiensReciHypo==\PfCRetiensReciSomme}{% Comme $\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2$, alors l'\'egalit\'e de Pythagore est v\'erifi\'ee. Donc le triangle $#2$ est rectangle en $\NomB$.}{% Comme $\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2$, alors l'\'egalit\'e de Pythagore n'est pas v\'erifi\'ee. Donc le triangle $#2$ n'est pas rectangle. }% }{% \xintifboolexpr{\PfCRetiensReciHypo==\PfCRetiensReciSomme}{% Comme $\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2$, alors le triangle $#2$ est rectangle en $\NomB$ d'apr\`es la r\'eciproque du th\'eor\`eme de Pythagore.}{% Comme $\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2$, alors le triangle $#2$ n'est pas rectangle\ifboolKV[ClesPythagore]{Faible}{.}{ d'apr\`es la contrapos\'ee du th\'eor\`eme de Pythagore.} }% }% }% \end{multicols} }{% \ifboolKV[ClesPythagore]{AllPerso}{% \RedactionReciPythagore% \RedactionCalculsReciPythagore% \RedactionConclusionReciPythagore% }{% \ifboolKV[ClesPythagore]{Perso}{\RedactionReciPythagore}{% Dans le triangle $#2$, $[\NomA\NomC]$ est le plus grand c\^ot\'e.% }% \PfCCalculsReciPythagore[#1]{#2}{#3}{#4}{#5}% \ifboolKV[ClesPythagore]{Egalite}{% \xintifboolexpr{\PfCRetiensReciHypo==\PfCRetiensReciSomme}{% Comme $\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2$, alors l'\'egalit\'e de Pythagore est v\'erifi\'ee. Donc le triangle $#2$ est rectangle en $\NomB$.}{% Comme $\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2$, alors l'\'egalit\'e de Pythagore n'est pas v\'erifi\'ee. Donc le triangle $#2$ n'est pas rectangle. }% }{% \xintifboolexpr{\PfCRetiensReciHypo==\PfCRetiensReciSomme}{% Comme $\NomA\NomC^2=\NomA\NomB^2+\NomB\NomC^2$, alors le triangle $#2$ est rectangle en $\NomB$ d'apr\`es la r\'eciproque du th\'eor\`eme de Pythagore.}{% Comme $\NomA\NomC^2\not=\NomA\NomB^2+\NomB\NomC^2$, alors le triangle $#2$ n'est pas rectangle\ifboolKV[ClesPythagore]{Faible}{.}{ d'apr\`es la contrapos\'ee du th\'eor\`eme de Pythagore.} }% }% }% }% }% }{% % [xlop] param\`etres de calcul \opcopy{#3}{A1}% \opcopy{#4}{A2}% \opcopy{\useKV[ClesPythagore]{Precision}}{pres}% \xintifboolexpr{#3<#4 || #3==#4}{% \xdef\PetitCote{#3}% \xdef\MoyenCote{#4}% \xdef\GrandCote{}% }{% \xdef\GrandCote{#3}% \xdef\MoyenCote{#4}% \xdef\PetitCote{}% Pour la personnalisation }% % On retient les noms des sommets \StrMid{#2}{1}{1}[\NomA]% \StrMid{#2}{2}{2}[\NomB]% \StrMid{#2}{3}{3}[\NomC]% \xdef\NomTriangle{\NomA\NomB\NomC}% \xdef\NomAngleDroit{\NomB}% \xdef\NomSommetA{\NomA}% \xdef\NomSommetC{\NomC}% % On trace une figure ou pas ? \ifboolKV[ClesPythagore]{FigureSeule}{% \xintifboolexpr{#3<#4 || #3==#4}{% \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2+#4^2),\useKV[ClesPythagore]{Precision})}}% }{% \xdef\ResultatPytha{\fpeval{round(sqrt(#3^2-#4^2),\useKV[ClesPythagore]{Precision})}}% }% \MPFigurePytha{\NomA}{\NomB}{\NomC}{#3}{#4}{\useKV[ClesPythagore]{Angle}}% }{% \ifboolKV[ClesPythagore]{Figure}{% \begin{multicols}{2}% {\em La figure est donn\'ee \`a titre indicatif.}% \[\MPFigurePytha{\NomA}{\NomB}{\NomC}{#3}{#4}{\useKV[ClesPythagore]{Angle}}\] \par\columnbreak\par% % On d\'emarre la r\'esolution \ifboolKV[ClesPythagore]{AllPerso}{% \RedactionPythagore% \RedactionCalculsPythagore% }{% \ifboolKV[ClesPythagore]{Perso}{% \RedactionCalculsPythagore% }{% \ifemptyKV[ClesPythagore]{Alias}{% \ifboolKV[ClesPythagore]{Egalite}{Comme le triangle $#2$ est rectangle en $\NomB$, alors l'\'egalit\'e de Pythagore est v\'erifi\'ee :}{Dans le triangle $#2$ rectangle en $\NomB$, le th\'eor\`eme de Pythagore permet d'\'ecrire :% }% }{}% }% \CalculsPythagore[#1]{#2}{#3}{#4}{} }% \end{multicols} }{% % On d\'emarre la r\'esolution \ifboolKV[ClesPythagore]{SansMots}{% \MPFigurePythaSansMots{\NomA}{\NomB}{\NomC}{#3}{#4}{\useKV[ClesPythagore]{Angle}}% }{% \ifboolKV[ClesPythagore]{AllPerso}{% \RedactionPythagore% \RedactionCalculsPythagore% }{% \ifboolKV[ClesPythagore]{Perso}{\RedactionPythagore}{% \ifemptyKV[ClesPythagore]{Alias}{% \ifboolKV[ClesPythagore]{Egalite}{Comme le triangle $#2$ est rectangle en $\NomB$, alors l'\'egalit\'e de Pythagore est v\'erifi\'ee :% }{Dans le triangle $#2$ rectangle en $\NomB$, le th\'eor\`eme de Pythagore permet d'\'ecrire :% }% }{} }% % \CalculsPythagore[#1]{#2}{#3}{#4}{}% }% }% }% }% }% }%