Démonstration du théorème de Pythagore - Garfield

Présentation
Cette activité a pour but de vous guider à travers une démonstration originale du théorème de Pythagore qui est dûe au 20e président des Etats-Unis, James Garfield, en 1876.
Etape n°1
Déplacer les points B et C. [br]Quelle est la nature du triangle ABC dans tous les cas ?
Pourrait-on obtenir n'importe quelles dimensions pour b et c en déplaçant les points B et C ?
Etape n°2
Quelle est la nature du triangle BCC' ?
Combien mesure l'aire du triangle bleu BCC' en fonction de a ?
Etape n°3 & 4
Que peut-on dire de l'angle rose et de l'angle vert en B ?[br][img]data:image/png;base64,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[/img]
Explique ton raisonnement pour calculer la somme des mesures des deux angles rose et vert.[br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAJsAAABvCAYAAAD7YrKDAAAQsklEQVR4Ae2dC1wVxR7HjyiigPIQFFCTyi75yOfVD2WJCmJiKF2ffAzFso+KKYhmmXK7oSFh+cCs1My0TA1NvYqPuprYwyIVQcUHKpAoojwEUnlI//v5H5hl9pzZwwH2nLPnMMtnP/9hdnbOzH+/+5uZ3Z1dVcehQ4GvlucDuz17QAWgtbb5+mvw9PQ0yarioFkeaI4ffaQFGYJnc+aMSSAjcHPYLEzZXd94gwlaswcPwGPkSA4bV1d51NUjIABaXrzIhM1lwQKTgobqxpXNgpTNbv9+JmhtN282OWgcNgsCzXHNGiZorZKTFQEah81CYHOJiGCCZlVcDB39/DhsvJ8mTz/NfcwYsL56lQmba3i4YkDjymYBymZ76BATtLYbNigKNA6bmcPm8MknTNBa/fKL4kDjsJkxbHgpg3WHoHlBAXTy8eGw8X6aPP00t7FjoUV2NhM217AwRYKmVjbn997j90bNTOFsf/iBCZrDunWKBU0NG0qxbWIiB85MgMOOP6v5bH38uKJBE2DDwltnZoKHvz+HTsHQtVu0iAla87w86PTcc+YDGzlb2r3zDgdOgcC5TZwILW7dYsLW/vXXFQ+aSNkIbGjtv/uOA6cw4LCZpI8RCUdGl8Akt0nmCxtWxDojgwOnEODafvEFE7TR+2qfjpznMk/xwKla3b3LrIj6zKmqApfISA6dCaFzjopiHp/HsgFy3Wphw0TLnJcpGjjV86+9Bq6//casEJHqNtu3c+BMAFyHV16B5hJicHCkGDRyAFc7rlYscKoRI0YArk9s307Ky7T4UB6/KCvPRVl9/djq55+Zx+L9d9igkcTrHJR5vU2ADYHrtXw5tCwqImXWss3Ky8F19mwOnRFUrs1XX2n5H1uasbt0g0Z2+tjhY8UpnAg2BG7QjBngcuoUKTPT4pOf+p6dPF391RDv6pAuDG2fvApQ4KwfbJjBh44fKgo4LdhIs+qZkMCsMKl8y3PnOHAGULgOoaFgde8e0/f/89UfNJJBVLsoxQAnCRtC98yKFWBdWkrKrWWb3b8P7adP59DJCF0ricFa3Jv1B40csJntZyoCOJ2wIXDPhoWBc0oKKTfTOnz2GQdOBuBw1E9aDtoGf9Nw0DDDsmZl8JLHSyYHrk7YEDj/gADoIjHDmjjF5tQpDlwjgHOKiWGC9vRFgFL7xsGGGV9qeQm6delmUuD0go3043qsWgXNHzxgOgWhsyopAbw2xAcF9RsUYFcEuyTkxKVt0uDGg0Yy3me3z3xgQ+i8584Fp3PnSPmZ1nH1ag6cvirn6ws2p08z/bg6XD7QyA+Y8i5DvZSNKJzf6NHQWWJCLDkr8Tl4rnB1K5y9xKh/6pfyg0aAC3IPMonCNQg2Al33+HiwqqggddCyVoWF4DZ+PIdOQuWc4uK0fIYn6zNpAGU2hoMtxSbF/GBD6AZGRoKDxPsliMo5ffABB04DONdZs6CZxIl60ttwoBG61ziuMTpwjVI2onC+L78MnSTmLxLgWh89yoGrAc5jxAiwSU0lx11kP5lleNDIDxr7cogssBHonsZ5jH//TeqiZZvfuQPugYGKg27Gf/5j1DLZ7d2r5Rs8KadvNB5oWICk1klGVTdZYUPoBixcCG0zMpjOJCrnHB1t1IOra6ACNUvSH3/AcCPcDXFcuZLpm/6nAP5uZlzYsCCRLpFGA0522BC4oTgo+P57plMJcLYHD5ocuGO//05YU9u7hYUQvny5wcrlOmcO0yfWFQCn+xkfNCxMdots84aNNKteEtPOCHDNc3NNNqMrKj5eAO1hWZkQxsD6b7+VHTj3UaOg5YULTNg+f800oJHCxDrFGgU4gygbgQ3tPxctgjaZmaReTGvsGV0+U6eK4Lp0/TrcKSgQxf10+jT4y9is2h04wKx72DrTgoaFKrUqhe5duhscOIPDhsANCQ4G92PHmM4mKmdnxBldNFU3cnPh15QU9ZqZk0NvgoJ792CeDJdtHNauZdb92V9NDxop2ErHlZYBG1G6f0jMEiLAtbhxQ/bmS3NwQPfTECYCGrHnMzLg/sOHIug27trV4HK5zJtHjqfI2t4HONdTObCVWJWAVxcvgwJnFGUjsKHtFxUFdn/+KXI8gY1Yl/nzG3xwNeGi/6f7aWXl5XAmPV0LNoTu97Q0wMECvfySkgK+r75ar3K5BwWB9ZUrzLpumaIc0EgBDX3f1OiwIXA+ISHgduIEqSPTyj2jK2jOHJoduJyZyQSNKBzarJs3RfvcKymBiNhYvYGzPXyYWbeIVcoDDQuaZZ1lWcpGq1znA+yXpBCFk2uidI8xY0TQ3Lh9u07QCHQXrl4FzdHqpt276wTO4dNPmaD5HFcmaKSwYa6Ge+WWSZQNgfMf5Q9PfPME2OVMBhWw3wlLoGvsjC66n1ZYXKw3aAQ4bFbzi4pEwP6WmgpDp01jQufy5pvk2Imswz2AS17Khu3H1j8aTN1MBlvvmN7gdtwNVOq/J0EF7G8tEeDafvkl88DSfTJWOGbDBgES7KclnztXb9gIdNm3bgl5YaDkr79gbkyMqFxu48aB9fXrIshIHbZPUjZopNBDOg4xCHAmgW3QjEHQKbET2Oba1sBWjZwKlpL6Mm3L8+dFB5YFFx03bckSERwXr11rMGgEOGxWEVp62ZiQIJQLHzggcNF24QfmARoW3lCXQUwCm9dGL3D5w0UDNALcBFCBjtFqVZVeM7qeDwmheYCcevTTCFhSFptVvGxCLydTU+FxiQch/X4wH9AQtsvWly1D2bzneqtVrWVRSwnYELpuoIJEpkIQtahrRldj+2lSoNHxdLO6X4KndvkA1x+X2Egqo0Ab6BEoO3BGV7Zu67qBc4qzDtCIwqGN1Qmc1IyuT3fuFESnvKICTp492+jmk4aMDmOzeqWyEqT6/bv/ZX6godMN8XClUWF7YdoLeqgaDRuGcbSaKwkdPu3aISRE6DPNj4sTQMMA3hGg4TBEeJjEDPbFy8wTNHR2qk2qeStbr9he4JIs1VfThIz+vxeoQPcjS/ihsNGzZ4tAw4uyhoCLznN6LvtECEg0X9DIme3d2VtW4IymbMPGDYMue7pA69zWejahNGwYbgYqYH8hmHR5fEpKBNhY9z1pSOQIx0hc4nC/BZDT0fxhk/vBSqPB1n9xf3A/6t5A0GjwQkEFBeTk07I4eTyzstLgirYzPR08ysu1fh/B/2+g+YOGFdthv8M8la3r1q7gmO4oA2wIXn9QwY/MA01UbnF2tkGBe16in/bevy0DNHRuhnWG+cE2eOrg6oFBoa7LHbR66RPGvOJ1AudXWGgQ4Kbevs383aA9lgMaqWDfx/rKBpxRmtEBbw0A92NyNKEsCF8HFZQQ32jZto8ewZG0NNmgi87K0voNVNMuWQB57S0PtpAOIeYFW49VPcApzUmmJpQFnDeogP3+WdKsRuvxSFFdg4ZtFy+Cq8TE4sMjLA80PKtinGLMCzbPBE+wval5H5QFTWPi7EAF7Md6CHAvFRQ0SuG8i4uZqrb8bcsEDSubYJ9gPrD5TPZR99da3G9hQGWjIZ0NKnjIhAKha19RAccbcEdhcl4eM88JeLOC0GyB9ozNGfOBbcDCAeBx1MNIoBHoBoMKknUyEHf9ut4qFyXxbc+uGQBFjpYNW37zfPOBrfva7jqe8CBwGMJiH3GTTuDG3b0rAHf+yhX1kyFFJSVQUVmpXouKiyE1Px9GPnrEzOfYUMsGjVS6x2M9ZAHO4KNR9fW1i3JdX2sIlBGggiriNy3buawMbublCXcepAJ4x5VuJT+K1IigN1pY2Lejr3nA5rnLE+yz7Y3cjGpC6Qsq0H4JtTsAnJGiixGPaXGfyV83HdDwDJvoNlH5sPmP9FcPDlrdaWVi2BC+9qCCrSJ12sEACptOnBBzrLgYDjK2HyoGuG/btGCb1X6W8mEbNnaYGjbrYmsFwEbUrnoyCr5eg17wFTODAOCpBw/g88uXwb6mn/YcAIhfP4PvtmpasL3l8pY8sK14ZgUYan1/0PsQPj8cQj8PhSlbpihoXQG3SyoF1u6XA0QkAEzZUrviN6Ksqqr7aZ0AQPQQeEbTgi3aOVoe2ETtioV1bCXrhreV6GUaG54rTwE8daUauE0/0TvgBTv2PpK/aca+jXOK47A1+MDitzrppQcDnN0AsBtg/9sAfVIAHvWidwAA+nuf0dVpYSKVD8JYk4cITEyD8bgPDeBnNfH05RQsF8mDTvtGTTxaOp6kpeuD+WE85k+nrUeZD0w7AIcPH4b4+HgRdNu2bVPHBwcHC/H+/v7qOEyP34Un67vvvqvuSokLQRfIUsNhFDj4ajZWPWuSZEwHmOG3CZY6L4Wqyiphx4MLDqrjMD7r5yx1fFJskhAX36f2/W8YxnS4YhpccB8Sh7You3oS9L7Z+4T4rYFbhd+j05795qw6Hi0dTxLjfiQe88MF8ydxaOtT5hOxJ9R5nDx5UoAHIbpx44Y6fsGCBUL8pEk4ObZ6IaChTVDPPGM52tLj8Ot29NKXAdwaAFgDsHtC9bS2UaNG0XvA5MmTBQfjWbt582YIDQ0V4vr06aOOw3gME8djGozDfUgc2lWrVqnjg4Jqv1EwZMgQIQ86bXh4uDoeLR2P+eKK+5F4zA/jMH8Sh9YUZcYhGvvMtuR4JxE3APPYPjjZ9TaQ57mWLl0q2ql3796ig0cfSB6ubT5pX6iC3YKhKa7ZF7JF8CwcslDkB/orKPhuEnpJT0/noFH9MRooXWGVro2WvG3WLPzgQO2Sk5MDM2dqf5cT43AbveC+luwbQ9WtycKGDsXRlOZy6dIldWd2165dgGHNBfcx1MGw9HybNGxeXl5w/Di+ME2/BdPiPpYOhaHq16RhI05dtgynruteMA1Jzy17AFCXXzhsNR3dwYMHw5IlS2DHjh1w4cIF9YphjMNtdTmSb68bQA5bA0ZVHKy6wWL5iMPGYTOaanPYOGwcNpYM87iGNV9K8RtXNq5sXNmUcjbycsinplzZuLJxZeOKIp+iKMWXXNm4snFlM8XZiE+Z1md98cUXYeDAgdC1a1ejHTBT+EWu3+TKRikb/Uiz7jul4q15eXnqJ2ERPLkOjCXmw2GjYKMPMD5GTRbNZ+9JusDAQNiyZQtJBufPn4e+feV7UyP5HUuxHLZGwEYgIBM/kLpDhw5xdZPwKYdNwjH6KBuB7ciRI4K63bx5k8Mm4VMOm4Rj6gPb+vXrBdhKS0s5bBI+5bBJOKY+sCUlVc8FReJQ5YjicSu+VshhayRsERERgqrhqDQgIIDDJuFTDpuEYzSVTfP626JFi2Dr1uoZ69nZ2fzSh4QfaXXnsEk4SRM2vPyhuWZmZkJycjLs3bsX1q5dC8OHD+eqJuFPhI7DJuEcTdjoM5QOT5gwAa5du6ZuSnFwgPvR23m4tt/GYWskbAjTnDlzhH4bBsaPH8+BY/iVw8ZwCgKkr7IR5crNzRWAS0xM5LAx/MphYzilIbBhf45eCITc8ma0TuWpj7L17NkT8vPzBdak7qU2dfC4ssmgbGFh9NsFgQ8SJHzKYZNwjL7KtnjxYkHRMLBz5846VbOpKhyHjYINL9zS19IIRXQcHcY7BmRJS0sDvNDbVEHSp94cNg3YNO8U1PW/n58f9OvXj0NG+VEKPA6bHk6Sch6Prx1p6uMLDhuHzWiqzGHjsHHY9JFlnqZ+zZip/cWVjSsbVzZTn4X89+VXzf8D75PmfJhBJQ0AAAAASUVORK5CYII=[/img]
Etape n°5
Justifie alors que les deux angles roses sont de même mesure.[br][img]data:image/png;base64,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[/img]
Etape n°6
On trace la perpendiculaire à (AB) passant par C', elle coupe (AB) en un point nommé D.
Etapes n°6 et 7
Justifier que l'angle en C' a la même mesure que l'angle vert.[br][img]data:image/png;base64,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[/img]
Etape n°8
Justifier que les triangles ABC et BDC' sont isométriques.
Etape n°9
On a codé les longueurs égales de la même couleur. [br]Combien mesure la longueur du segment [AD] ?[br][img]data:image/png;base64,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[/img]
Aire du quadrilatère ACC'D (méthode 1)
Quelle expression ci-dessous correspond à l'aire du quadrilatère ACC'D ?
Expliquer le découpage utilisé et le calcul pour obtenir la réponse précédente.
Etape n°10
Justifier que ACC'D est un trapèze.
Combien mesure la hauteur du trapèze ACC'D ?
Aire du quadrilatère ACC'D (méthode 2)
On rappelle que l'aire d'un trapèze se calcule avec la formule suivante :[br](moyenne des deux bases)x(hauteur).[br]Quelle expression correspond ici à ce calcul ?
Regarde cette vidéo où Manu Houdart présente la démonstration de Garfield
Complète les deux calculs comme Manu Houdart dans la vidéo.
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Information: Démonstration du théorème de Pythagore - Garfield