{"version":3,"file":"6G32-JWN0zz4O.js","sources":["../../src/exercices/6e/6G32.js"],"sourcesContent":["import { angle, angleOriente } from '../../lib/2d/angles.js'\nimport { arc } from '../../lib/2d/cercle.js'\nimport { afficheLongueurSegment } from '../../lib/2d/codages.js'\nimport { distancePointDroite, droite } from '../../lib/2d/droites.js'\nimport { point, pointSurDroite, tracePoint } from '../../lib/2d/points.js'\nimport { nommePolygone, polygone } from '../../lib/2d/polygones.js'\nimport { longueur, segmentAvecExtremites } from '../../lib/2d/segmentsVecteurs.js'\nimport { labelPoint, latexParPoint } from '../../lib/2d/textes.js'\nimport { homothetie, rotation, symetrieAxiale } from '../../lib/2d/transformations.js'\nimport { miseEnEvidence, texteEnCouleurEtGras } from '../../lib/outils/embellissements'\nimport { choisitLettresDifferentes } from '../../lib/outils/aleatoires.js'\nimport { sp } from '../../lib/outils/outilString.js'\nimport { texNombre } from '../../lib/outils/texNombre.js'\nimport Exercice from '../Exercice.js'\nimport { fixeBordures, mathalea2d } from '../../modules/2dGeneralites.js'\nimport { calculANePlusJamaisUtiliser, gestionnaireFormulaireTexte, listeQuestionsToContenu, randint } from '../../modules/outils.js'\nexport const titre = 'Use axial symmetry preservation properties'\n\n// Gestion de la date de publication initiale\nexport const dateDePublication = '25/01/2023'\n\n/**\n * Utiliser les propriétés de la symétrie pour répondre à des questions\n * @author Eric Elter\n */\n\nexport const uuid = '65bd7'\nexport const ref = '6G32'\nexport default function SymetrieAxialeProprietes () {\n  Exercice.call(this) // Héritage de la classe Exercice()\n  this.titre = titre\n  this.consigne = ''\n  this.spacing = 2\n  this.nbQuestions = 3\n  this.nbCols = 1\n  this.nbColsCorr = 1\n  this.sup = '5'\n  this.sup2 = true\n\n  this.nouvelleVersion = function () {\n    this.listeQuestions = [] // Liste de questions\n    this.listeCorrections = [] // Liste de questions corrigées\n    this.autoCorrection = []\n    /*\n    let typesDeQuestionsDisponibles = []\n    if (!this.sup) { // Si aucune liste n'est saisie\n      typesDeQuestionsDisponibles = rangeMinMax(1, 4)\n    } else {\n      if (typeof (this.sup) === 'number') { // Si c'is a number it means the number was entered in the address bar\n        typesDeQuestionsDisponibles[0] = contraindreValeur(1, 5, this.sup, 5)\n      } else {\n        typesDeQuestionsDisponibles = this.sup.split('-')// Sinon on créé un tableau à partir des valeurs séparées par des -\n        for (let i = 0; i < typesDeQuestionsDisponibles.length; i++) { // on a un tableau avec des strings : ['1', '1', '2']\n          typesDeQuestionsDisponibles[i] = contraindreValeur(1, 5, parseInt(typesDeQuestionsDisponibles[i]), 5) // parseInt en fait un tableau d'entiers\n        }\n      }\n    }\n    if (compteOccurences(typesDeQuestionsDisponibles, 5) > 0) typesDeQuestionsDisponibles = rangeMinMax(1, 4) // Teste si l'utilisateur a choisi tout\n    typesDeQuestionsDisponibles = combinaisonListes(typesDeQuestionsDisponibles, this.nbQuestions)\n*/\n\n    const typesDeQuestionsDisponibles = gestionnaireFormulaireTexte({\n      max: 4,\n      defaut: 5,\n      nbQuestions: this.nbQuestions,\n      melange: 5,\n      saisie: this.sup\n    })\n\n    for (let i = 0, texte, texteCorr, objetsEnonce, a, b, d, A, B, C, D, E, F, ptRef1, ptRef2, Aarc, Barc, Carc, ALabel, BLabel, CLabel, nbpoints, noms, cpt = 0; i < this.nbQuestions && cpt < 50;) {\n      texte = ''\n      texteCorr = ''\n      objetsEnonce = []\n      a = randint(-10, 10)\n      b = randint(-10, 10, a)\n      d = droite(a, b, 0, '(d)')\n      switch (typesDeQuestionsDisponibles[i]) {\n        case 1 :\n          nbpoints = 4\n          noms = choisitLettresDifferentes(nbpoints, 'QWX', true)\n          A = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[0])\n          while (distancePointDroite(A, d) < 1) A = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[0])\n          B = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[1])\n          while ((distancePointDroite(B, d) < 1) || (longueur(A, B) < 1) || (longueur(symetrieAxiale(A, d), B) < 1)) B = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[1])\n          C = symetrieAxiale(A, d, noms[2])\n          D = symetrieAxiale(B, d, noms[3])\n          texte += `The segments $[${A.nom}${B.nom}]$ and $[${C.nom}${D.nom}]$ are symmetric with respect to $(d)$ and $${A.nom}${B.nom}=${texNombre(longueur(A, B, 1))}${sp()}\\\\text{cm}$ . What is the length of segment $[${C.nom}${D.nom}]$?`\n          texte += this.sup2 ? ' Justify.<br>' : '<br>'\n          objetsEnonce.push(d, segmentAvecExtremites(A, B), segmentAvecExtremites(C, D), nommePolygone(polygone([A, B]), A.nom + B.nom), nommePolygone(polygone([C, D]), C.nom + D.nom), afficheLongueurSegment(A, B))\n          texte += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce, { pixelsParCm: 40, scale: 1, style: 'margin-top: 40px' })), objetsEnonce)\n          texteCorr += `The segments $[${A.nom}${B.nom}]$ and $[${C.nom}${D.nom}]$ are symmetric with respect to $(d)$.<br>`\n          texteCorr += 'However, the symmetric of a segment is a segment of the same length.<br>'\n          texteCorr += `So the segments $[${A.nom}${B.nom}]$ and $[${C.nom}${D.nom}]$ have the same length and $${miseEnEvidence(C.nom + D.nom + '=' + texNombre(longueur(A, B, 1)))}$${sp()}${texteEnCouleurEtGras('cm')}.<br>`\n          break\n        case 3 :\n          nbpoints = 6\n          noms = choisitLettresDifferentes(nbpoints, 'QWX', true)\n          A = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[0])\n          while (distancePointDroite(A, d) < 1) A = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[0])\n          B = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[1])\n          while ((distancePointDroite(B, d) < 1) || (longueur(A, B) < 1) || (longueur(symetrieAxiale(A, d), B) < 1)) B = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[1])\n          C = pointSurDroite(droite(A, B), B.x + 1, noms[2])\n          D = symetrieAxiale(A, d, noms[3])\n          E = symetrieAxiale(B, d, noms[4])\n          F = symetrieAxiale(C, d, noms[5])\n          texte += `The points $${D.nom}$, $${E.nom}$ and $${F.nom}$ are the respective symmetrics of $${A.nom}$, $${B.nom}$ and $${C.nom}$ with respect to $(d)$. The points $${A.nom}$, $${B.nom}$ and $${C.nom}$ are aligned. Are the $${D.nom}$, $${E.nom}$ and $${F.nom}$ points?`\n          texte += this.sup2 ? ' Justify.<br>' : '<br>'\n          objetsEnonce.push(d, tracePoint(A, B, C, D, E, F), labelPoint(A, B, C, D, E, F))\n          texte += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce, { pixelsParCm: 40, scale: 1, style: 'margin-top: 40px' })), objetsEnonce)\n          texteCorr += `The points $${D.nom}$, $${E.nom}$ and $${F.nom}$ are the respective symmetrics of $${A.nom}$, $${B.nom}$ and $${C.nom}$ with respect to $(d)$ and are aligned.<br>`\n          texteCorr += 'However, axial symmetry preserves alignment.<br>'\n          texteCorr += `So the $${miseEnEvidence(D.nom)}$${texteEnCouleurEtGras(',')}$${miseEnEvidence(E.nom)}$${texteEnCouleurEtGras(' And')}$${miseEnEvidence(F.nom)}$ ${texteEnCouleurEtGras(' are aligned')} points also.<br>`\n          break\n        case 2 :\n          nbpoints = 6\n          noms = choisitLettresDifferentes(nbpoints, 'QWX', true)\n          A = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[0])\n          while (distancePointDroite(A, d) < 1) A = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[0])\n          B = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[1])\n          while ((distancePointDroite(B, d) < 1) || (longueur(A, B) < 1) || (longueur(symetrieAxiale(A, d), B) < 1)) B = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[1])\n          C = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[2])\n          while ((distancePointDroite(C, d) < 1) || (longueur(A, C) < 1) || (longueur(symetrieAxiale(A, d), C) < 1) || (longueur(C, B) < 1) || (longueur(symetrieAxiale(B, d), C) < 1) || (angle(A, B, C) < 30) || (angle(B, A, C) < 30) || (angle(A, C, B) < 30)) C = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[2])\n          D = symetrieAxiale(A, d, noms[3])\n          E = symetrieAxiale(B, d, noms[4])\n          F = symetrieAxiale(C, d, noms[5])\n          texte += `The points $${D.nom}$, $${E.nom}$ and $${F.nom}$ are the respective symmetrics of $${A.nom}$, $${B.nom}$ and $${C.nom}$ with respect to $(d)$. What is the length of segment $[${D.nom}${F.nom}]$?`\n          texte += this.sup2 ? ' Justify.<br>' : '<br>'\n          objetsEnonce.push(d, polygone([A, B, C], 'green'), nommePolygone(polygone([A, B, C]), A.nom + B.nom + C.nom), polygone([D, E, F], 'brown'), nommePolygone(polygone([D, E, F]), D.nom + E.nom + F.nom), afficheLongueurSegment(A, B), afficheLongueurSegment(A, C), afficheLongueurSegment(C, B))\n          texte += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce, { rxmin: -1, rymin: -1, rxmax: 1, rymax: 1, pixelsParCm: 40, scale: 1, style: 'margin-top: 40px' })), objetsEnonce)\n          texteCorr += `The segments $[${A.nom}${B.nom}]$ and $[${C.nom}${D.nom}]$ are symmetric with respect to $(d)$.<br>`\n          texteCorr += 'However, the symmetric of a segment is a segment of the same length.<br>'\n          texteCorr += `So the segments $[${A.nom}${B.nom}]$ and $[${C.nom}${D.nom}]$ have the same length and $${miseEnEvidence(C.nom + D.nom + '=' + texNombre(longueur(A, B, 1)))}$${sp()}${texteEnCouleurEtGras('cm')}.<br>`\n          break\n        case 4 :\n          nbpoints = 6\n          noms = choisitLettresDifferentes(nbpoints, 'QWX', true)\n          A = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[0])\n          while (distancePointDroite(A, d) < 1) A = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[0])\n          B = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[1])\n          while ((distancePointDroite(B, d) < 1) || (longueur(A, B) < 6 || (longueur(symetrieAxiale(A, d), B) < 1))) B = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[1])\n          C = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[2])\n          while ((distancePointDroite(C, d) < 1) || (longueur(A, C) < 6) || (longueur(symetrieAxiale(A, d), C) < 1) || (longueur(C, B) < 6) || (longueur(symetrieAxiale(B, d), C) < 1) || (angle(A, B, C) < 30) || (angle(B, A, C) < 30) || (angle(A, C, B) < 30)) C = point(calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), calculANePlusJamaisUtiliser(randint(-80, 80, 0) / 10), noms[2])\n          D = symetrieAxiale(A, d, noms[3])\n          E = symetrieAxiale(B, d, noms[4])\n          F = symetrieAxiale(C, d, noms[5])\n          texte += `The points $${D.nom}$, $${E.nom}$ and $${F.nom}$ are the respective symmetrics of $${A.nom}$, $${B.nom}$ and $${C.nom}$ with respect to $(d)$. What is the measure of the angle $\\\\widehat{${D.nom}${F.nom}${E.nom}}$?`\n          texte += this.sup2 ? ' Justify.<br>' : '<br>'\n          objetsEnonce.push(d, polygone([A, B, C], 'green'), nommePolygone(polygone([A, B, C]), A.nom + B.nom + C.nom), polygone([D, E, F], 'brown'), nommePolygone(polygone([D, E, F]), D.nom + E.nom + F.nom))\n          ptRef1 = (longueur(A, B) < longueur(C, B)) ? A : C\n          ptRef2 = (longueur(A, B) < longueur(C, B)) ? C : A\n          Barc = homothetie(ptRef1, B, 2 / 10)\n          BLabel = rotation(homothetie(ptRef1, B, 2 / 10 + 1 / longueur(ptRef1, B)), B, angleOriente(ptRef1, B, ptRef2) / 3)\n          BLabel.positionLabel = 'center'\n          objetsEnonce.push(arc(Barc, B, angleOriente(ptRef1, B, ptRef2)), latexParPoint(`${angle(ptRef1, B, ptRef2, 0)}\\\\degree`, BLabel, 'black', 12, 20, ''))\n          ptRef1 = (longueur(A, C) < longueur(C, B)) ? A : B\n          ptRef2 = (longueur(A, C) < longueur(C, B)) ? B : A\n          Carc = homothetie(ptRef1, C, 2 / 10)\n          CLabel = rotation(homothetie(ptRef1, C, 2 / 10 + 1 / longueur(ptRef1, C)), C, angleOriente(ptRef1, C, ptRef2) / 3)\n          CLabel.positionLabel = 'center'\n          objetsEnonce.push(arc(Carc, C, angleOriente(ptRef1, C, ptRef2)), latexParPoint(`${angle(ptRef1, C, ptRef2, 0)}\\\\degree`, CLabel, 'black', 12, 20, ''))\n          ptRef1 = (longueur(A, C) < longueur(A, B)) ? C : B\n          ptRef2 = (longueur(A, C) < longueur(A, B)) ? B : C\n          Aarc = homothetie(ptRef1, A, 2 / 10)\n          ALabel = rotation(homothetie(ptRef1, A, 2 / 10 + 1 / longueur(A, ptRef1)), A, angleOriente(ptRef1, A, ptRef2) / 3)\n          ALabel.positionLabel = 'center'\n          objetsEnonce.push(arc(Aarc, A, angleOriente(ptRef1, A, ptRef2)), latexParPoint(`${180 - angle(A, ptRef2, ptRef1, 0) - angle(A, ptRef1, ptRef2, 0)}\\\\degree`, ALabel, 'black', 12, 20, ''))\n          texte += '<br>' + mathalea2d(Object.assign({}, fixeBordures(objetsEnonce, { rxmin: -1, rymin: -1, rxmax: 1, rymax: 1, pixelsParCm: 40, scale: 1, style: 'margin-top: 40px' })), objetsEnonce)\n          texteCorr += `The angles $\\\\widehat{${A.nom}${C.nom}${B.nom}}$ and $\\\\widehat{${D.nom}${F.nom}${E.nom}}$ are symmetric with respect to $(d)$.<br>`\n          texteCorr += 'However, the symmetrical of an angle is an angle of the same measure.<br>'\n          texteCorr += `So the angles $\\\\widehat{${A.nom}${C.nom}${B.nom}}$ and $\\\\widehat{${D.nom}${F.nom}${E.nom}}$ have the same measure and $\\\\widehat{${D.nom}${F.nom}${E.nom}} = ${angle(D, F, E, 0)}\\\\degree$.<br>`\n          break\n      }\n      if (this.questionJamaisPosee(i, a, b)) { // Si la question n'a jamais été posée, on en crée une autre\n        this.listeQuestions.push(texte)\n        this.listeCorrections.push(texteCorr)\n        i++\n      }\n      cpt++\n    }\n\n    listeQuestionsToContenu(this)\n  }\n  this.besoinFormulaireTexte = ['Type of questions', 'Numbers separated by hyphens\\n1: Length of a single segment\\n2: Length of one segment among others\\n3: Alignment of points\\n4: Angle\\n5: Blending']\n  this.besoinFormulaire2CaseACocher = ['Justification 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