{"version":3,"file":"_RelationDeThales-DGafyaOD.js","sources":["../../src/exercices/4e/_RelationDeThales.js"],"sourcesContent":["import { angle, angleOriente } from '../../lib/2d/angles.js'\nimport { point, pointAdistance, pointSurSegment } from '../../lib/2d/points.js'\nimport { polygone } from '../../lib/2d/polygones.js'\nimport { longueur } from '../../lib/2d/segmentsVecteurs.js'\nimport { texteParPoint } from '../../lib/2d/textes.js'\nimport { homothetie, similitude } from '../../lib/2d/transformations.js'\nimport { triangle2points2longueurs } from '../../lib/2d/triangle.js'\nimport { creerBoutonMathalea2d } from '../../lib/outils/modales.js'\nimport { texteGras } from '../../lib/format/style'\nimport { creerNomDePolygone } from '../../lib/outils/outilString.js'\nimport Exercice from '../Exercice.js'\nimport { mathalea2d } from '../../modules/2dGeneralites.js'\nimport { context } from '../../modules/context.js'\nimport { listeQuestionsToContenu, randint, calculANePlusJamaisUtiliser } from '../../modules/outils.js'\n\nexport const titre = 'Write a Thales relation'\n\n/**\n * Relation de Thalès\n * @author Sébastien LOZANO\n*/\nexport default function RelationDeThales () {\n  Exercice.call(this) // Héritage de la classe Exercice()\n\n  this.consigne = ''\n  this.nbQuestions = 1\n  this.nbCols = 1\n  this.nbColsCorr = 1\n  this.sup = 1 // Triangles imbriqués / configuration papillon / les 2\n\n  this.nouvelleVersion = function (numeroExercice) {\n    this.listeQuestions = [] // Liste de questions\n    this.listeCorrections = [] // Liste de questions corrigées\n    let listeDeNomsDePolygones = []\n    this.autoCorrection = []\n    if (this.level === 4) {\n      this.sup = 1\n    }\n    const premiereQuestionPapillon = randint(0, 1) // Pour alterner les configurations et savoir par laquelle on commence\n\n    for (let i = 0, texte = '', texteCorr = '', cpt = 0; i < this.nbQuestions && cpt < 50;) {\n      // this.autoCorrection[i] = {}\n      if (i % 3 === 0) { // Toutes les 3 questions, on repart à zéro sur les noms des polygones\n        listeDeNomsDePolygones = ['Q.D.']\n      }\n      const nomDesPoints = creerNomDePolygone(5, listeDeNomsDePolygones)\n      listeDeNomsDePolygones.push(nomDesPoints)\n      const nomA = nomDesPoints[0]\n      const nomB = nomDesPoints[1]\n      const nomC = nomDesPoints[2]\n      const nomM = nomDesPoints[3]\n      const nomN = nomDesPoints[4]\n      const ab = randint(5, 10)\n      const ac = randint(5, 10, ab)\n      const bc = randint(Math.max(ab - ac, ac - ab) + 1, ab + ac - 1, [ab, ac]) // Pas de triangle isocèle ou équilatéral\n      const A = point(0, 0, nomA)\n      const B = pointAdistance(A, ab, nomB)\n      const ABC = triangle2points2longueurs(A, B, ac, bc)\n      ABC.id = `M2D_${numeroExercice}_${i}_1`\n      const C = ABC.listePoints[2]\n      C.nom = nomC\n      let k = calculANePlusJamaisUtiliser(randint(3, 8, 5) / 10)\n      if (parseInt(this.sup) === 2) {\n        k *= -1\n      }\n      if (parseInt(this.sup) === 3 && ((i + premiereQuestionPapillon) % 2 === 0)) {\n        k *= -1\n      }\n      const M = homothetie(A, C, k)\n      const N = homothetie(B, C, k)\n      const MNC = polygone(M, N, C)\n      MNC.id = `M2D_${numeroExercice}_${i}_2`\n      const m = pointSurSegment(M, N, -0.5)\n      const n = pointSurSegment(N, M, -0.5)\n      const marqueNomM = texteParPoint(nomM, m, 'medium', 'black', 1, 'middle', true)\n      const marqueNomN = texteParPoint(nomN, n, 'medium', 'black', 1, 'middle', true)\n      const a = pointSurSegment(A, B, -0.5)\n      const b = pointSurSegment(B, A, -0.5)\n      const marqueNomA = texteParPoint(nomA, a, 'medium', 'black', 1, 'middle', true)\n      const marqueNomB = texteParPoint(nomB, b, 'medium', 'black', 1, 'middle', true)\n      let c\n      if (k < 0) {\n        if (angle(A, C, N) < angle(N, C, A)) {\n          c = similitude(A, C, -angleOriente(A, C, N) / 2, 1 / longueur(A, C))\n        } else {\n          c = similitude(A, C, -angleOriente(N, C, A) / 2, 1 / longueur(A, C) * 0.5)\n        }\n      } else {\n        c = similitude(A, C, -180 + angleOriente(A, C, B) / 2, 1 / longueur(A, C) * 0.5)\n      }\n      const marqueNomC = texteParPoint(nomC, c, 'medium', 'black', 1, 'middle', true)\n\n      texte = 'In the following figure:'\n      if (k > 0) {\n        texte += `\n        <br> $\\\\leadsto ${nomM}$ is on $${'[' + nomC + nomA + ']'}$,\n        <br> $\\\\leadsto ${nomN}$ is on $${'[' + nomC + nomB + ']'}$,`\n      } else {\n        texte += `<br> $\\\\leadsto$ the lines $(${nomA + nomM})$ and $(${nomB + nomN})$ are secant in $${nomC}$,`\n      }\n\n      texte += `<br> $\\\\leadsto$ the lines $(${nomA + nomB})$ and $(${nomM + nomN})$ are parallel.<br>Write a Thales relation.<br>`\n\n      texte += mathalea2d({\n        xmin: Math.min(A.x, B.x, C.x, M.x, N.x) - 1.5,\n        ymin: Math.min(A.y, B.y, C.y, M.y, N.y) - 0.8,\n        xmax: Math.max(A.x, B.x, C.x, M.x, N.x) + 1.5,\n        ymax: Math.max(A.y, B.y, C.y, M.y, N.y) + 0.8,\n        scale: 0.5\n      },\n\n      ABC, MNC, marqueNomA, marqueNomB, marqueNomC, marqueNomM, marqueNomN\n      )\n\n      const epaisseurTriangle = (k < 0) ? 2 : 6 // En cas de configuration papillon il est inutile de changer l'épaisseur\n      const boutonAideMathalea2d = creerBoutonMathalea2d(numeroExercice + '_' + i,\n        `if (!document.getElementById('M2D_${numeroExercice}_${i}_1').dataset.colorie == true || (document.getElementById('M2D_${numeroExercice}_${i}_1').dataset.colorie == 'false')){\n          document.getElementById('M2D_${numeroExercice}_${i}_1').style.stroke = 'blue';\n          document.getElementById('M2D_${numeroExercice}_${i}_2').style.stroke = 'red';\n          document.getElementById('M2D_${numeroExercice}_${i}_1').style.opacity = .5;\n          document.getElementById('M2D_${numeroExercice}_${i}_1').style.strokeWidth = ${epaisseurTriangle};\n          document.getElementById('M2D_${numeroExercice}_${i}_2').style.opacity = 1;\n          document.getElementById('M2D_${numeroExercice}_${i}_2').style.strokeWidth = 2;\n          document.getElementById('M2D_${numeroExercice}_${i}_1').dataset.colorie = true;\n          document.getElementById('btnMathALEA2d_${numeroExercice}_${i}').classList.add('active');\n        } else {\n          document.getElementById('M2D_${numeroExercice}_${i}_1').style.stroke = 'black';\n          document.getElementById('M2D_${numeroExercice}_${i}_2').style.stroke = 'black';\n          document.getElementById('M2D_${numeroExercice}_${i}_1').style.opacity = 1;\n          document.getElementById('M2D_${numeroExercice}_${i}_1').style.strokeWidth = 1;\n          document.getElementById('M2D_${numeroExercice}_${i}_2').style.opacity = 1;\n          document.getElementById('M2D_${numeroExercice}_${i}_2').style.strokeWidth = 1;\n          document.getElementById('M2D_${numeroExercice}_${i}_1').dataset.colorie = false;\n          document.getElementById('btnMathALEA2d_${numeroExercice}_${i}').classList.remove('active');\n  \n        }\n        `,\n        'Color the 2 triangles')\n\n      if (k > 0) {\n        texteCorr = `In the $${nomA + nomB + nomC}$ triangle:<br> $\\\\leadsto$ $${nomM}\\\\in${'[' + nomC + nomA + ']'}$,<br> $\\\\leadsto$ $${nomN}\\\\in${'[' + nomC + nomB + ']'}$,<br> $\\\\leadsto$ $(${nomA + nomB})/ /(${nomM + nomN})$,<br> therefore according to Thales' theorem, the triangles $${nomA + nomB + nomC}$ and $${nomM + nomN + nomC}$ have proportional lengths.`\n      } else {\n        texteCorr = `$\\\\leadsto$ The lines $(${nomA + nomM})$ and $(${nomB + nomN})$ are intersecting in $${nomC}$,<br> $\\\\leadsto$ the lines $(${nomA + nomB})$ and $(${nomM + nomN})$ are parallel,<br>so according to Thales' theorem, the triangles $${nomA + nomB + nomC}$ and $${nomM + nomN + nomC}$ have proportional lengths.`\n      }\n      texteCorr += '<br><br>'\n      if (context.isHtml) {\n        texteCorr += `$\\\\dfrac{\\\\color{red}${nomC + nomM}}{\\\\color{blue}${nomC + nomA}}=\\\\dfrac{\\\\color{red}${nomC + nomN}}{\\\\color{blue}${nomC + nomB}}=\\\\dfrac{\\\\color{red}${nomM + nomN}}{\\\\color{blue}${nomA + nomB}}$`\n      } else {\n        texteCorr += `$\\\\dfrac{${nomC + nomM}}{${nomC + nomA}}=\\\\dfrac{${nomC + nomN}}{${nomC + nomB}}=\\\\dfrac{${nomM + nomN}}{${nomA + nomB}}$`\n      }\n\n      texteCorr += context.isHtml ? '<br>' : '\\\\medskip'\n      texteCorr += `<br>${texteGras('To note:')}<br>We could also write:`\n      if (context.isHtml) {\n        texteCorr += `$\\\\dfrac{\\\\color{blue}${nomC + nomA}}{\\\\color{red}${nomC + nomM}}=\\\\dfrac{\\\\color{blue}${nomC + nomB}}{\\\\color{red}${nomC + nomN}}=\\\\dfrac{\\\\color{blue}${nomA + nomB}}{\\\\color{red}${nomM + nomN}}$`\n      } else {\n        texteCorr += `$\\\\dfrac{${nomC + nomA}}{${nomC + nomM}}=\\\\dfrac{${nomC + nomB}}{${nomC + nomN}}=\\\\dfrac{${nomA + nomB}}{${nomM + nomN}}$`\n      }\n\n      if (context.isHtml) {\n        texte += `<br><div style=\"display: inline-block;margin-top:20px;\">${boutonAideMathalea2d}</div>`\n      }\n\n      if (this.listeQuestions.indexOf(texte) === -1) {\n        // If the question has never been asked, we create another one\n        this.listeQuestions.push(texte)\n        this.listeCorrections.push(texteCorr)\n        i++\n      }\n      cpt++\n    }\n    listeQuestionsToContenu(this)\n  }\n  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