import{E as T,c as x,r as n,bB as L,aj as C,w as c,ay as o,aL as d,m as v,p as k,l as y}from"./index-XCg2QAX4.js";import{T as Q}from"./Triangle-1uP0ZINz.js";const D=!0,E="qcm",G=!0,F="AMCHybride",J="Constructibility of triangles via lengths or angles",O="10/12/2023";function R(){T.call(this),this.sup=1,this.sup2=!1,this.nbQuestions=3,this.beta="",this.nbCols=1,this.nbColsCorr=1,this.listePackages="bclogo";let u;this.nouvelleVersion=function(){let N;if(this.exo===this.beta+"5G21-1"?N=!this.interactif||x.isAmc?"Justify whether the given lengths allow the triangle to be constructed":"Indicate whether, with the information provided, the triangle can be constructed":N=!this.interactif||x.isAmc?"Justify whether the given angles allow the triangle to be constructed":"Indicate whether, with the information provided, the triangle can be constructed",this.consigne=N+".",this.exo===this.beta+"5G21-1")if(this.sup===1)u=[1,2,3];else if(this.sup===3){const g=n(1,3);this.nbQuestions===1?u=[4]:this.nbQuestions===2?u=[4,g]:this.nbQuestions===3?u=[4,g,g%3+1]:u=[4,1,2,3]}else u=[4];else if(this.exo===this.beta+"5G31-1")if(this.sup===1)u=[5,6,7];else if(this.sup===3){const g=n(5,7);this.nbQuestions===1?u=[8]:this.nbQuestions===2?u=[8,g]:this.nbQuestions===3?u=[8,g,(g-4)%3+5]:u=[8,5,6,7]}else u=[8];else u=[1,2,3,4,5,6,7,8];this.sup2||(L(u,2),L(u,6));const w=C(u,this.nbQuestions);this.listeQuestions=[],this.listeCorrections=[],this.autoCorrection=[];for(let g=0,a,r,m,b,f,l,i,$,A=0;g<this.nbQuestions&&A<50;){const e=new Q,t=[];switch(w[g]){case 1:for(;!e.isTrueTriangleLongueurs();)m=n(2,20),b=n(2,20),f=n(2,20),e.l1=m,e.l2=b,e.l3=f;a=`${e.getNom()} such that ${e.getLongueurs()[0]} $= ${e.l1}$ cm;`,a+=`${e.getLongueurs()[1]} $= ${e.l2}$ cm and ${e.getLongueurs()[2]} $= ${e.l3}$ cm.`;for(let s=0;s<3;s++)t.push({longueur:e.getLongueurs()[s],cote:e.getCotes()[s],valeur:e.getLongueursValeurs()[s]});t.sort(function(s,h){return s.valeur-h.valeur}),r=`Suppose we can construct a triangle ${e.getNom()} with these measurements.`,r+=`<br>In the triangle ${e.getNom()}, ${t[2].cote}, which measures $${t[2].valeur}$ cm, is the longest side.`,r+=`<br> Moreover ${t[0].longueur} + ${t[1].longueur} = $${t[0].valeur}$ cm + $${t[1].valeur}$ cm = $${o(t[0].valeur+t[1].valeur)}$ cm.`,r+=`<br> We see that ${t[0].longueur} + ${t[1].longueur} > ${t[2].longueur}.`,r+=`<br> ${d("We can therefore construct the triangle")}$${v(e.getNom().substring(1,e.getNom().length-1)+".")}$`;break;case 2:for(;!e.isPlatTriangleLongueurs();)m=n(2,20),b=n(2,20),f=o(m+b),e.l1=m,e.l2=b,e.l3=f;a=`${e.getNom()} such that ${e.getLongueurs()[0]} $ = ${e.l1}$ cm;`,a+=`${e.getLongueurs()[1]} $= ${e.l2}$ cm and ${e.getLongueurs()[2]} $= ${e.l3}$ cm.`;for(let s=0;s<3;s++)t.push({longueur:e.getLongueurs()[s],cote:e.getCotes()[s],valeur:e.getLongueursValeurs()[s]});t.sort(function(s,h){return s.valeur-h.valeur}),r=`Suppose we can construct a triangle ${e.getNom()} with these measurements.`,r+=`<br>In the triangle ${e.getNom()}, ${t[2].cote}, which measures $${t[2].valeur}$ cm, is the longest side.`,r+=`<br> Moreover ${t[0].longueur} + ${t[1].longueur} = $${t[0].valeur}$ cm + $${t[1].valeur}$ cm = $${t[2].valeur}$ cm too.`,r+=`<br> ${d("We can therefore construct the triangle")}$${v(e.getNom().substring(1,e.getNom().length-1))}$${d(", it is a flat triangle.")}`,r+=`<br><br>${d("Only one such triangle exists")}, this is the ${t[2].cote} segment on which the point is placed`,t[0].longueur.split("")[2]===t[2].cote.split("")[1]||t[0].longueur.split("")[2]===t[2].cote.split("")[2]?r+=`${t[0].longueur.split("")[1]}`:r+=`${t[0].longueur.split("")[2]}`,r+=".";break;case 3:for(m=n(2,20),b=n(2,20),f=n(2,20),e.l1=m,e.l2=b,e.l3=f;e.isTrueTriangleLongueurs()||e.isPlatTriangleLongueurs();)m=n(2,20),b=n(2,20),f=n(2,20),e.l1=m,e.l2=b,e.l3=f;a=`${e.getNom()} such that ${e.getLongueurs()[0]} $= ${e.l1}$ cm;`,a+=`${e.getLongueurs()[1]} $= ${e.l2}$ cm and ${e.getLongueurs()[2]} $= ${e.l3}$ cm.`;for(let s=0;s<3;s++)t.push({longueur:e.getLongueurs()[s],cote:e.getCotes()[s],valeur:e.getLongueursValeurs()[s]});t.sort(function(s,h){return s.valeur-h.valeur}),r=`Suppose we can construct a triangle ${e.getNom()} with these measurements.`,r+=`<br>In the triangle ${e.getNom()}, ${t[2].cote}, which measures $${t[2].valeur}$ cm, is the longest side.`,r+=`<br> Moreover ${t[0].longueur} + ${t[1].longueur} = $${t[0].valeur}$ cm + $${t[1].valeur}$ cm = $${o(t[0].valeur+t[1].valeur)}$ cm.`,r+=`<br> We see that ${t[0].longueur} + ${t[1].longueur} < ${t[2].longueur}, the given lengths therefore do not allow us to satisfy the triangular inequality.`,r+=`<br> ${d("We cannot therefore construct the triangle")}$${v(e.getNom().substring(1,e.getNom().length-1)+".")}$`;break;case 4:for(;!e.isTrueTriangleLongueurs();)m=n(2,20),b=n(2,20),f=n(2,20),e.l1=m,e.l2=b,e.l3=f;a=`${e.getNom()} such that ${e.getLongueurs()[0]} $= ${e.l1}$ cm;`,a+=`${e.getLongueurs()[1]} $= ${e.l2}$ cm and whose perimeter is $${e.getPerimetre()}$ cm.`;for(let s=0;s<3;s++)t.push({longueur:e.getLongueurs()[s],cote:e.getCotes()[s],valeur:e.getLongueursValeurs()[s]});t.sort(function(s,h){return s.valeur-h.valeur}),r=`Suppose we can construct a triangle ${e.getNom()} with these measurements.`,r+=`<br>Since the perimeter is $${e.getPerimetre()}$ cm then the third length is ${e.getLongueurs()[2]} = $${e.getPerimetre()}$ cm - $${e.l1}$ cm - $${e.l2}$ cm = $${e.l3}$ cm.`,r+=`<br> So in the triangle ${e.getNom()}, ${t[2].cote}, which measures $${t[2].valeur}$ cm, is the longest side.`,r+=`<br> Moreover ${t[0].longueur} + ${t[1].longueur} = $${t[0].valeur}$ cm + $${t[1].valeur}$ cm = $${o(t[0].valeur+t[1].valeur)}$ cm.`,r+=`<br> We see that ${t[0].longueur} + ${t[1].longueur} > ${t[2].longueur}`,r+=`<br> ${d("We can therefore construct the triangle")}$${v(e.getNom().substring(1,e.getNom().length-1))}$.`;break;case 5:for(;!e.isTrueTriangleAngles();)l=n(0,180,[0,180]),i=n(0,180,[0,180]),$=o(180-l-i),e.a1=l,e.a2=i,e.a3=$;a="",r="",a=`${e.getNom()} such that ${e.getAngles()[0]} $= ${e.a1}\\degree$;`,a+=`${e.getAngles()[1]} $= ${e.a2}\\degree$ and ${e.getAngles()[2]} $= ${e.a3}\\degree$.`;for(let s=0;s<3;s++)t.push({angle:e.getAngles()[s],valeur:e.getAnglesValeurs()[s]});t.sort(function(s,h){return s.valeur-h.valeur}),r=`Suppose we can construct a triangle ${e.getNom()} with these measurements.`,r+=`<br>In the triangle ${e.getNom()}, ${t[0].angle} + ${t[1].angle} + ${t[2].angle} = $${t[0].valeur}\\degree + ${t[1].valeur}\\degree + ${t[2].valeur}\\degree = ${o(t[0].valeur+t[1].valeur+t[2].valeur)}\\degree$.`,r+="<br> We see that the sum of the three angles of the triangle is indeed $180\\degree$.",r+=`<br> ${d("We can therefore construct the triangle")}$${v(e.getNom().substring(1,e.getNom().length-1))}$.`;break;case 6:for(;!e.isPlatTriangleAngles();)l=n(0,180),i=n(0,180),$=o(180-l-i),e.a1=l,e.a2=i,e.a3=$;a="",r="",a=`${e.getNom()} such that ${e.getAngles()[0]} $= ${e.a1}\\degree$;`,a+=`${e.getAngles()[1]} $= ${e.a2}\\degree$ and ${e.getAngles()[2]} $= ${e.a3}\\degree$.`;for(let s=0;s<3;s++)t.push({angle:e.getAngles()[s],valeur:e.getAnglesValeurs()[s]});t.sort(function(s,h){return s.valeur-h.valeur}),r=`Suppose we can construct a triangle ${e.getNom()} with these measurements.`,r+=`<br>In the triangle ${e.getNom()}, ${t[0].angle} + ${t[1].angle} + ${t[2].angle} = $${t[0].valeur}\\degree + ${t[1].valeur}\\degree + ${t[2].valeur}\\degree = ${o(t[0].valeur+t[1].valeur+t[2].valeur)}\\degree$.`,r+="<br> We see that the sum of the three angles of the triangle is indeed $180\\degree$.",r+=`<br> ${d("We can therefore construct the triangle")}$${v(e.getNom().substring(1,e.getNom().length-1))}$.`,r+=`<br> Two of the three angles of the triangle are worth $0\\degree$,$${v(e.getNom().substring(1,e.getNom().length-1))}$`+d(" is therefore a flat triangle.");break;case 7:for(l=n(0,180),i=n(0,180),$=n(0,180),e.a1=l,e.a2=i,e.a3=$;e.isTrueTriangleAngles();)l=n(0,180),i=n(0,180),$=n(0,180),e.a1=l,e.a2=i,e.a3=$;a=`${e.getNom()} such that ${e.getAngles()[0]} $= ${e.a1}\\degree$;`,a+=`${e.getAngles()[1]} $= ${e.a2}\\degree$ and ${e.getAngles()[2]} $= ${e.a3}\\degree$.`;for(let s=0;s<3;s++)t.push({angle:e.getAngles()[s],valeur:e.getAnglesValeurs()[s]});t.sort(function(s,h){return s.valeur-h.valeur}),r=`Suppose we can construct a triangle ${e.getNom()} with these measurements.`,r+=`<br>In the triangle ${e.getNom()}, ${t[0].angle} + ${t[1].angle} + ${t[2].angle} = $${t[0].valeur}\\degree + ${t[1].valeur}\\degree + ${t[2].valeur}\\degree = ${o(t[0].valeur+t[1].valeur+t[2].valeur)}\\degree$.`,r+="<br> If the triangle were constructible, the sum of the three angles would be worth $180\\degree$,",r+=" However, it is not the case.",r+=`<br> ${d("We cannot therefore construct the triangle")}$${v(e.getNom().substring(1,e.getNom().length-1)+".")}$`;break;case 8:{const s=n(0,1),h=["triple","quadruple","quarter"];let M="";switch(a="",r="",r=`Suppose we can construct a triangle ${e.getNom()} with these measurements.`,s){case 0:switch(l=n(0,180),e.a1=l,M=h[n(0,2)],a+=`${e.getNom()} such that ${e.getAngles()[0]} $= ${c(e.a1)}\\degree$;`,M){case"triple":i=o((180-l)/4),$=o(3*i);break;case"quadruple":i=o((180-l)/5),$=o(4*i);break;case"quarter":i=o(4*(180-l)/5),$=o(i/4);break}e.a2=i,e.a3=$,a+=`${e.getAngles()[1]} $= ${c(e.a2)}\\degree$ and ${e.getAngles()[2]} is the ${M} of ${e.getAngles()[1]}.`;for(let p=0;p<3;p++)t.push({angle:e.getAngles()[p],valeur:e.getAnglesValeurs()[p]});r+=`<br>In the ${e.getNom()} triangle, ${t[2].angle} is the ${M} of ${t[1].angle} = $${c(t[1].valeur)}\\degree$ hence ${t[2].angle} = $${c(t[2].valeur)}\\degree$.`;break;case 1:switch(i=n(0,180),e.a2=i,M=h[n(0,2)],a+=`${e.getNom()} such that ${e.getAngles()[1]} $= ${c(e.a2)}\\degree$;`,M){case"triple":l=o((180-i)/4),$=o(3*l);break;case"quadruple":l=o((180-i)/5),$=o(4*l);break;case"quarter":l=o(4*(180-i)/5),$=o(l/4);break}e.a1=l,e.a3=$,a+=`${e.getAngles()[0]} $= ${c(e.a1)}\\degree$ and ${e.getAngles()[2]} is the ${M} of ${e.getAngles()[0]}.`;for(let p=0;p<3;p++)t.push({angle:e.getAngles()[p],valeur:e.getAnglesValeurs()[p]});r+=`<br>In the ${e.getNom()} triangle, ${t[2].angle} is the ${M} of ${t[0].angle} = $${c(t[0].valeur)}\\degree$ hence ${t[2].angle} = $${c(t[2].valeur)}\\degree$.`;break}r+=`<br>So ${t[0].angle} + ${t[1].angle} + ${t[2].angle} = $${c(t[0].valeur)}\\degree + ${c(t[1].valeur)}\\degree + ${c(t[2].valeur)}\\degree = ${c(t[0].valeur+t[1].valeur+t[2].valeur)}\\degree$.`,r+="<br> We see that the sum of the three angles of the triangle is indeed $180\\degree$.",r+=`<br> ${d("We can therefore construct the triangle")}$${v(e.getNom().substring(1,e.getNom().length-1))}$.`;break}}if(this.listeQuestions.indexOf(a)===-1){const s=[{texte:`The ${e.getNom()} triangle is constructible`,statut:!(w[g]===2||w[g]===7),feedback:this.exo===this.beta+"5G21-1"?"Take the sum of the smallest lengths and compare it to the longest length.":"Adds the angles of the triangle."},{texte:`The ${e.getNom()} triangle is not constructible`,statut:w[g]===2||w[g]===7,feedback:this.exo===this.beta+"5G21-1"?"Take the sum of the smallest lengths and compare it to the longest length.":"Adds the angles of the triangle."},{texte:`We cannot know if the triangle ${e.getNom()} is constructible or not`,statut:!1,feedback:this.exo===this.beta+"5G21-1"?"Take the sum of the smallest lengths and compare it to the longest length.":"Adds the angles of the triangle."}];this.interactif&&(this.autoCorrection[g]={enonce:a,propositions:s,options:{ordered:!1,lastChoice:2}}),x.isAmc&&(this.autoCorrection[g]={enonce:N+" :<br>"+a,options:{numerotationEnonce:!0},propositions:[{type:"AMCOpen",propositions:[{texte:"",numQuestionVisible:!1,statut:2,feedback:""}]},{type:"mthMono",enonce:"Following your justification, fill in the appropriate box among the following:",propositions:s,options:{ordered:!1,lastChoice:2}}]}),this.interactif&&(a+=k(this,g).texte),this.listeQuestions.push(a),this.listeCorrections.push(r),g++}A++}y(this)},this.exo===this.beta+"5G21-1"?this.besoinFormulaireNumerique=["Difficulty level",2,`1: 3 lengths
2: 2 lengths and perimeter
3: Combination`]:this.besoinFormulaireNumerique=["Difficulty level",2,`1: 3 angles
2: 2 angles and the 3rd depending on the 1st or 2nd
3: Combination`],this.besoinFormulaire2CaseACocher=["Accept flat triangle"]}export{G as amcReady,F as amcType,O as dateDeModifImportante,R as default,D as interactifReady,E as interactifType,J as titre};
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