Tag: triângulos

Decomposição de um triângulo pela altura referente à hipotenusa 0

Decomposição de um triângulo pela altura referente à hipotenusa

Decomposição de figuras - Teorema de Pitágoras

var parameters = { "id": "ggbApplet", "width":725, "height":322, "showMenuBar":false, "showAlgebraInput":false, "showToolBar":false, "customToolBar":"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6", "showToolBarHelp":false, "showResetIcon":true, "enableLabelDrags":false, "enableShiftDragZoom":false, "enableRightClick":false, "errorDialogsActive":false, "useBrowserForJS":false, "preventFocus":false, "language":"pt", // use this instead of ggbBase64 to load a material from GeoGebraTube // "material_id":12345, "ggbBase64":"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// is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View var views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0}; var applet = new GGBApplet(parameters, '5.0', views); window.onload = function() {applet.inject('ggbApplet')};

 
1 – O triângulo [ABC] é rectângulo em A e [AD] é a altura referente à hipotenusa.…

1

Calcula o valor de x em cada triângulo

Decomposição de figuras - Teorema de Pitágoras: Matematicamente Falando 8 - Parte 1 Pág. 25 Ex. 15

Enunciado

Calcula o valor de x em cada um dos seguintes triângulos (a unidade de comprimento é o centímetro):

Resolução >> Resolução

var parameters = { "id": "ggbApplet", "width":648, "height":157, "showMenuBar":false, "showAlgebraInput":false, "showToolBar":false, "customToolBar":"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6", "showToolBarHelp":false, "showResetIcon":true, "enableLabelDrags":false, "enableShiftDragZoom":false, "enableRightClick":false, "errorDialogsActive":false, "useBrowserForJS":false, "preventFocus":false, "language":"pt", // use this instead of ggbBase64 to load a material from GeoGebraTube // "material_id":12345, "ggbBase64":"UEsDBBQACAgIADp4H0cAAAAAAAAAAAAAAAAtAAAAYzg4MWIxNmQ2ODNhYjVhZDg2ZGFlMzQ2OGY5YTY4OWJccGFnMjUtMTUuanBnvXl3VFRNn+aFBhqQLDk1SQERyTk0QbJEyVlRyTmD0A2IpCYHEYmS4yuSM5KD5CgIAo02DSKpyaGX99uZ3dn5ZvbM7B9b9zzn3Kp7b1U9deuX6oddxK4BFJqqGqoADi4A4NxeAHYZUAYICQjABPiEYDCYiIiQmISalOTOHRIGqrvk1CyMEFYWRmZmNq5H3GwcDzmZmXkkeB8KComKikK4peQkhWUfiYgK/90JDhEREckdEnpSUnphdmZ24f92wXYDlIRAHO5TEA4HgEuJA6LEwfYBkNt54uP8owD/UnBwQXj4BGBCIuI7ty80UAC4OCAQLh4IHx8P7/ZpyO1zAI8Sn4pdSJHgrv4zMIcntXBYcgEhp1LtFxqDqX0ukede4UTEtHT0DIz37nPz8D4QFROXkJSSVn6soqqmrqH51NDI2MTUzNzuxctX9g6OTt4+vn7+AYFBEW8i30ZFx8SmpKalZ7zLfJ/1sbCouKS0rLzic119Q2NTc0trT29f/8Dg0PDI9Mzs3PzC4rel9Q3k5s9fqC309sHhEeb45PTs/OJvXjgACOdfy3/Ii/KWFy4eHggP/DcvHFz/v1+gxMNnFyKgUtQHP/O8yyEcRkitlFxQ+4WIU8Rgn+a51xQxLZfo+r2Dv6n9g9l/jVj4/xOz/0Xsf/NaAkhAOLc/D0QJQIHTi8LAYII88AdvdtPTinfE6viZPNwsBOrDW9LZxKV/rfDnpFD6+uJ9Hqnt4edUyzLZqVUOb4d7qa/hegklRxVqedd0RV/JVfN/zaiIYX2EUPKknsoZGhB4h2CmHCeXRSSRLcUO7a/MLnTSTj/6Q+SI+vxWg2jbLOnuRdZCPm4sz38ZJCH2pq7smLlDvC7XDi2lJx/83Ej8faQuOyR35v+ylJ1aGjmZqqp7cJfZ5VI52+OOLZK7k9Sri0J+vDGLz1pn34LUXED8ZdJgrbhGcwZz2YDXN3rmzecfXO1eFl2pNDRM5b9d4q3i/qDf1KiXjHodaogojN98D8ipg6fh0toCeokm09ViPLSPY3/dSzdQjLJE7D4bJ9xSK6t+8OuKGXzC/JWMM1W/MwXq41yu/uy3d1IIYU0KnJjn438JQscQCjTjk0rawool85HRdjXRbYSJ5Eq4d72/HAGZE5+VqvIG09iDn0mpxFZLwiRu0VdVpbOVCFQCl/Va1sjMn6fqB+Jd18Xu0qPBsv4UVsWVrVpADIVai2IvJ/hch3ysmUzbfNTqtWJMYQzCL+tpzAv01+lylcEaNu/d5BlONhYVan0F/P8GGBgHEska3Em0xfqovghP4Pe37abwEqgqsiVEhuFRKFOoib3zXBdL6DVK6DlE7Uq3ckn4S9zN8MiulGb2uDRrDIsEuwEgmrkpBQplEr99NRJNKslZDp4tgB639GMswPPfQLUoxVjdWAzX4nJqUEQ9ZmgiVBdlmD9V5fL7T3X9ot1M6CSTsFlP8udaMAry6A4JKilwJ2v+I5zX1MwC3Uh7Yjx1bryvWvsYntpgaEuSqwvqsPq/DKapjCniAjQkQR2B820HpEt+jfvbXAUaxp2Zd8mudpfgXlfH7q1gTtEPWl4FRNpLD1CF0/Pgt+2K7hv8QgLPlakLEP60PyPoX7AYJi8snuL5oC1Wyr5ri/7u/xjLG/33AA/SO9I7qpqEb1ewJXXs/WcNvyXqu3kvQaxzfp+OPzCNdigrZUw+4nfPcnzfQvx29cW4sMiRNILc8iSfdORBXjoswc12ogyOBQ58ZvDP0cH0F4pYYCH/zqwRpM4JgqHQvQJDkGrfGsgvCLmvzyBIBbqyCqh9116ZwN81Tf49z7F9qLra2ST+0oO8bzUJsJnsEE6b/ZIPMnVYQEgq6rouEQvE/N0fea01bNIYeXOthgX6pkNij27CFyCnfwRu7sOlxpzWBjfitByOmTKruVK+/6jytlVYnkjCGTDU3Pn5CYwHCEpQBUuPi9PZ3zxvgpxu33709lM7J8i0FTyrRocFKBUYRY2V0e9QXM6nO7k9fKFQSXR8oROJ5IF4RdeffufrZ/mkFXyEW+YxWOB9kxlEvQoLnPVzn5CVYgFlvwYsEHrbcM4Klyirgvxm0b15u+t8c22GBQ7lQEqziqj+rOETodvqQSyw+rH2bWJQIekGv/5NuQs0TSlbVI2TvMrJfQ/1AAtsPeABKYwy6tSKlPnjVaSO4iyAljmPyndoWeh+L9XTOft68yRIUWYEvr85+W4nS95mYQjoq1D/E4zd/qow32q1vIhH/m5qUvoTfImzrdENauGor5zY4y8+WC2X7vWY3LqwjHyWBKj0L641ioyoDbEIf2NbI9b+RsYrUf5VbQNGubzKos+17C0bWSM6GnGTWAevLbSl9tUPX/zy3EsoFuNOdvaxt89498R1f6U/sd78ifgo0SnLl9+9bBcLH1Ydmk6akh1T+khKtMsMtL/EgA5Y25ELq20OV5ROojtWqVqulcukU06CnhxCbElqqjqC+p8JT6Vqgoy4Nmdkag3LlLKtJMq/TVnGR8W4uYjR+8CoVUhzMF+p5rc5QscCdCQNQpGbSDuvgC9SNa2tOsDHWJ7/NqrGdI0/Tz20vtRvtgh+sb2bOpEPyuD+BKQaiiVSWzj666MnVU+X+kbM7xBKeUkTeE+LThxIsHhmG1kJ9IoMB7PWbcj0d83dvX6sKeT6clgyPrhJUljiqwKLkObaq21jRiyAcHEjWcbk8H6U1049kJtCvY/GAsZv7DYhEtyeSFePSoaGNooxIn0Gnil8sJvkEljX/ac1OizBO/bnsTupmaUTX8V5HMiOyq2n6s26IvcCcxAGHYuqBsuI+q956hf43iuUdCfXqED7GzifGH/WtWfEm31uXacqSfJeUoBV49QSERF73Oac+Wj3eUtT+svwF+TM0V4M6kNsF88zmAJ2N0wL4g3E6I2MukHTLXxm4PDjyhDetPth5U+M++sS6yxrHz6T2qzM+VpaO4SOnc/6aWwvFlRRrSZa5Terr+LwnFpfBaD5UOEE1vqU8dvMajV6/4lxNKuSTFIRAlkDlofPp1PjDJkGfGtw5tkT3SN1pvM7BDWqW9+S+OUZsTtfjQV6dMuwwOT7v7DAD2PYVbLeNitL7p1zX3fSUZaMYnZ+Tzz4h+CvyOvnCfGH+8jkjCEpMfmIDa0Qa+NPWXQzx8G+K94l46pnF69H1MiyEcIHQ+Pk1HDdM41jyMVdMSxw+WcCC6TwwtbvzXZtaS907bVBb9RvR9WBXWCyba9WZC70PTNt9pO3M5FfslBI/iQssBwbrkvpvO4NCRcTP3EeVYBhHGveden2hEUgIIPzcdGbeX2dfMNEa3x1EV9CdBbJp+KVVnkOai/zyJmPrszHmm/Mar6ukT+70BPayYVKmzAMQqjOkIjX0KdYwLMMdpYFjpH1gP1SRIT4lnWdZf1WW0ArDpDpgL1z0yzJlG+oyJncBq/YJnEWc5ygNxwfOw50YzGXdO0t+yGfOew8bhYMAiWxQC5MczcYcVwDG6Bs72RqUU8u8q4jLuS62kgrmm4x3CgWo/Xq3fCrTCF/Wz0gJ6YCvbzn9uWvgIoAY5X9InYWZR7XJwSoWeq1S8ajIcyY8lc8x9Oi416LTmh60J9E8m8YLfo7QkIKMUf23HcSvMcDLuYNnTRNWr4hCjTTOz60ZIgl0nnmES0l2pxl3f42plJSm/6o0shqtQUjyJVbq8DPHa0fP6YbW3q8IwwPHCGH/Kag7yymxyfXc1rXBRuFiWdJjhGzOUa1WOCjs48tzpH95MVUcsS4HBZoU+n+cukeVzcQVUgWvD1tDzkjV3d//QyuGldwiTJ+hwWSd14n56F3TFnZF7hmHm6Ej0Drt5tqnn2OqEH9GYN7REvZLZca8DRToK3Z5tyuNMTjYSXmA/vd97MstErfPx8+N4pTzRPahIt0j/kaxayvUMnd0RGsLwkeNh3z9+kmyH16monMx7C85XMrU1Sh1sP5P0CTXr1D4WBueBHZ0xY9OExtJyCSS0Pt/0oS0COwiXF3q7nfuP/ng2DCzRVtlt6is4V+X0riSQw7XSl/3rpYbck3C3QGhemSyk9FXDwVvGycbV2ui9ThHbNQpukal40PenPEjbVlNCm/a8QHww778n7nc/kPc53WRGRD9A0WRwTpx0uDwooDcQe+MpPGJCncOX9x7YQFft6IaRIhQ5T+0BhTDdRmvEZ5yHwCb8KkW0MccdQMauvnHuaOnKzy7r48t+alexCITLRci1hmqHEkKF+bI2p01eqNXQTfq3G5m48FamofiWTv6QWHWb2T77oOkjqGmt+9Q4G+iCwptyPdTUPLVY0wSlFsCoq5tTD9ILdatOmsXH+fMv/zR8gYIop2AbbKhXOoHnA+eKqqiDd3TdfnsUNy8lnpRLoIdM3R4yU7dEkL+fEE4/kFWeKUStmlQv30v6igv875BrPQftkTqKElTFuzT9n9ZqT2cPATcxYwUyOPtOk8IJk2CzBW7+NZfuRrb3Xw2EuZS/nGXF0o7w8iQcdTjwVqehBBO0+D6SA5zHKS2KsJQ6M+XVaomQ7KHgagKsMJqwsS7gQUxtLPcqjGNeiRAYAHWIdXnCA0Zv0aqhSr6MBS8r7J0nJk+VcOFmj/HcidOqiYC1Tn/srSAC4u9POUB58/UH3kpXZU8W6DtjZN55KT/hXbCwTzrdtirCgJBs3Q6OrZNgrXJ8fQeJj50wwNYfZigY5Bqb2LOdKn2vXzPqPx0odsJwuE+rMXQRGLEUOcBcDcH6/AnZkleCDyMJ/MrjcoZ5Zu5szdJKmx8FXYWrMdFoD4ba6/2MnpZTINQpzWfG7Zo9xKrFzqF8seda00h+Y88wriyrysTtAUXI/yxNBIRDUkVy++t6ZtbI/8KuGXoLp1j8VwLUnNQ01PsUJJfOtjrO0/1HhU9VnQqE1TvNvc9AbBD3fvO64Z4N9DKy2ghCgQRxNPPpn0jz66Jfyv0v6xV12PLPk7a6l2w18N4byEHI4oJ8FaA7/Q9/u+v4JVq3i74+/WNy4IFk1qFnPFqpDUlIYTylJahs34uhNUiic0MZa8IbDQ8V+Ry2RZ497Lt05m9SIglyyaHJ/hXDjIZ20PcYY+mXM5DhZr/5xzPzJBUracRZmsordZ7PUmZTiO3LWTgtV3LGBjjkOPTkRr5BbO/NXAzck6mLyjQD7hPo44PdnIEsntUlYc4p6hBvLDJdFZIuNC6l4Aitp7BqrrRCADmgw2ImU1RU1VFUc/4QygTNO9qcMDHcEadvZMovgN64fjB945Cw9wHHGYUCL/hIsk9sAfoX6hUhN7EAmSFwaAl5RkYQosB5catWhfzfDlxhrTQ7D2nZaZ9wJ5xbtCJgfTVOZ1ak0vSS6xdKJLia5eUzoU2t0S+p7azTKObxfgrN3S2pLad1FEwK96wpa0nBxh7z5ntwlqz3t/dGXpQ2MwrXaQ0HHy2T8g+Eke7SKE/3jk+B2XNyMrHRj/s5cHvt+xQ9Kt5w7/t96eCbT6LEy0fNelQDzPrU3Gls5f/vHjTeCObcog9AFcyxYDJE+a8Fejm7TLxvwdbd8NHA4tSstUELbcM03FAg/HkW1uFpE9TZLAtnP0jGbAjKW2a2cIk3ZyqvaTn26vIHyWdoU8P/VuZSBgqLxhJ+bYYrH9nr1oxcxjiH5L3NumJjQCQ8qOr0qmMDzIUJO7uspk4VC9Fm8XzkU5ECtpBAJChDQ+3QeVeu+oEsgg5es7Wg38N4pe8hT7zT6iKKDkKBlYVODazGa9bg26dtrCLeu7nZSDJd2q7YtE29+3caSdXJA9wktuGwtAkQok3SzRN3nrWrOYX+/kf2gqqXXyAMiEztXjqJoAp0FLoWH2lNUL8qzVi8XfWaChc4uZ1HQpMHfsykSjbjED6lwPfM9+484KRwBmj7pKX6ZWK8SAPS44t4hg4qKcEC9dypqM3Om3U85XCuulYXd/d+aTQ9LPKhxgY9Y3lOF8abyVAeJG4rXa5Wc+zKLscd8XEb5Pjh7alfxob0GyPS8XYumgySt1Mm5tyDZplCDydOf4Y0axD+u+iBiqJv6HoP2HiMoyv9V2mV9ptKgA5pRgE3bxrrKzlN3fsqJv+USfv5P+WnlIQkHcDf1Z6PVDYoUpeFMP/9qu78DxNKZ4cbmzoEoz8mNdXHysoMTICueTz4eBKLgTC19vynWrnH2fBBGsEv442OSUFp6k2VO6RXB0xOw3/uAmPn/RwTgeP0seTXb+h0umOOeyPSHwlXxXBp+N7Oz3Z90TOxqJ4+8kIahYHV7AAwdzY2iX65ltgJpOlf+Wj9c9aDNQYRMYZyeiRqXNZhn9zYt8/WJ29fUrE4R67gtbkZr1dLAk94wkNP1p8NYeBl0yXcPZChV1ODmsfL22hkAxsGJwCuEwyPw7etT5SX4uRg8nbOJ8zMv8OHIgsQLWY1LcyzVd9Zxfc15kbBbYFEZECt8P4E5psVywyI2CXDuJhDs0U5itLjuJC1p/G6mz0KVP4aXYH1FVpHFr9pkIP+6LI5GVKtd83XjDdCfjBnJil5QrKFid3P3Mqt80/N+c7pBpPd2vfPTxYj7MQ/Ta7NNL5nM6OJXSSOF2qIcEad+Rcb07pVr5ymjpytJo6Q4FW6DLL5QXivWFi6QPFwW99yCbT01CrW8H7qh1HYU1Z5RyJ1N0wrDrj7qBHz3dazfMv9Lhc3eW51Md7gxLHk9obhYs+JKTWcZBqNd/Z0Y2zSMtVTezXXMU+rRnfl1GyRkiTMyZhcutlUkiFqfpmxlQh8eFIM7zqdwz6LqiLCuUWAHAmZHEYMqGFdmUzvzwIrlewneuBtEGqLy/gpCFgVwHcx0/+/wpRVS8XZl1Qa9rC+/TUxDKJPwaD6LGe6FvK23TsHQrV/zJzQirzK+VOEmBkThA4/fNGnUGdFaiTnDUDD/jmvorB73hX4/mv6sZAPRSO92DxV4xfF0xvnyZnAlWkk6No96cqb+qBgiNXlfhksBkzYZZXsgiTGxKBmXNX1Z5P7mf/twoUNlttdvLO2wBrfPFaw0kdby3o64gm9cT7gkHr6NVYRc3GDghM0r+eGRnwXuHEb4//kFEjRM/RHNbvnESsgZO4gqFQ9bvdfAp9zFOTVUlLXfbzz7KVnzpQvAkJff94H7ZqNAEMalMrznVFqNjWLEEXapU7iEaTio7NirUDVok6yZ2xCl3dMSPLxJvrH2opxTGqbJVIU1cp0Kj9Pep111qgykFfJatfzkH6zsg+Nx6PwdVFer6dfohbcba2piIRyXmj66kno5kNe8fjsamlI0Nw1j6tLZhTnxDPWENbjiwZ9kJ/xyQaAy7+52zOhPRW6zCATxW29MJjrhPIP0aHjRJ8C7K59XU7r3g951TZVYj9u15Uivsv+Uo1YhlcCzU5FqxgLR+gtQFo6DcNgFLEOu1w964EFpxEPrIeyGhvt1e7toBJE2v57SQQpRcFPBxhf5yJL+T6OIoYnfXnKX1+kGatdK2Cb4W0evm0xpBYNQ2ceHWsnXEAo5rMGnBYCRUZ7Yd5zqEpxt1a7sY1ViuO8pvTWY8t+fexdSgzegS/C7YjY5hV9M777n0hUESoVzIFosDKH1WVsrfuUyjMsAN/XCv6F4NP9fEN7fhiUeFaV59LDsTYKnhyiDyGPZ5rpRphxef5vIZmmf+EB5R2DOlJbCQv2JmlfapviIfxVRp2/fOmx/Xe35nWG9+U2exaqHxcwIk+MCM2WeIe3k5TFtQYqtGXIDKKiDoFxM5jfBDg9eNFz0lo4GJ3C4R0NbX3hMjHp6I523shmz/Schu8mnqIeORXos6GxjnQ6XQVgX41ilkuF/XkEfTW2rzKN3ujpP5bIW5DA/hiABEtnpalOld6vAEMCtt83ZTYmr7hu29GIsZdfR+c/gkFZFp0ukQRGqU2ZeF15I47mVFQF9Mg2mN6Nhdhjidlc/BuYqkUswfkYk83sPfvQAWSwo1VzwPRcZBKh7Dx3o0CvQATjeNuBoIqhskDJ1wMqFnPpqYnBoPKUNOTuVhASs2alSTDUojIbS+3XYq+zZ4qweyw8ndNiKy7RGXsUSAV5A/pjDhA4wY+BJOf7e/tZceabraM1c8BEByUfc6Ao7LqsAnkTXlZe8ovgQUDo/+xr1n+bAK+qaJ+3ry/Rc80ve71fZHGQHPUycSh5OkQb9Kxw6Zj5mbWFHzdTaPp+rHHl2ZLS6jazUYHHNHaGI+5Sf94NlMUB+TCWtUROV69wvAUOrqDFyQIGscMOu3IlwKdXoscDwVroiKfTqorxo4+DrUB0dLvzbCoDZr/I9YyupLXo5c5OKJFEqu1tSaedatSuDn/kC1zJgv7l5tW5p3oPtiau4L6/jJXCZ6qZp8QRwvQpaOSqY+abZ50SuLr/OtkW3nje80TguSYGJy9P54pyWZTBhjcFTD3u4HR7tmxPJ2xhvlEAdVEgO7MgYp1e3qIc4ugqbtN/9qKmlSK7aT0T2L9NwtudtPaTra8f2H1hmG8L8ZPtNP5PI57nc2EdnYejx/4Z9Dily6t7oT9VmDMWBhNIlAGbJH9+sBkY5HHyStAXCyGHWsQkci7msFzhWm8KZ+ryzkPcWjnG5p+jQvy94ZwqZdvhUhcD8z1DnOcxhq73LVW8Ipn83qISErg3cSRNPQ0Wf99HExpfiDdITQIqECtfhYC7FQ9kZjGYhPc86lIQ6vY+aPcYBZ9AiCQs3INpBEjlwsX80m9CZ9fPuGNftHZ3X+SkiEscdHvdHMRz0op5GukoMjnEFZYr+4jegGpmHRtkv7mYZoQwaXUpe9p9my2tMqMhbJQ4Nshov2iuFCcPncdNXDAZnmRTqHX4e5PCgFiQFm2/QhTlnQZIK00Spu4rajLgM9soNNZEbtk9bWHn6RjUM0kOLK8IRXT61zWjVoLXly452qVSt/bPWXFlx81tCxXHtIsLvLcb8DeYehT9uiQP0HizY/v3CHuansZ9Hy+T6iOAGXob7mh4c/dOpyTw593i5Rr3DWrgN7xiJHyE6+RF93emdnxgx5yMy9r1Fn7jV0Z0FXUwXj3l9spZGik3cD/OZRRm3yPHPPfbJU+ErNhwRdXSeUTLiIIJWU44IdtSay2oGB1OK0flIiTnRKyxy6DyMPV5XfbrdQJje/gGsASfg+vkpYQDf2hivBarkw+WWCiqTDio4y6IJyMlwRj4r0NpbTfDVD0dDWjeZKFnUVekeSIpza0WKrznV3nHDNuN9gpopjxiVlnuUnzfs49Z/v32fWCXGXP9S4ctr9dw6Z5WmMbyBmWb0ac5bian38lVawpefdgFYjTg/PecwJqJwaJ6dqWCCmoetMNf+R6KVH6vZhpev30rQmeqnzgwzO+HzE1WJNtaFqRUWBIQkPCMeZr3eJy5wgI0ODPev5gEVclB7jxiupQCaW4au3+C6wVIOB+7qnoQ2arjrjRC9jnd+YcRyeEgxhAdP+u6zFmTT0e/3WNyGVWXNVAm7HbcGXwQqjpdQ81Wy4mzKh+3ay1HoM/ra0clGibNKWGNkw1ZAu4iesIuGOgUX4hKticzXvRoxg9zleknkhBeBqLrZHP+TnfK1sCv6SPos82jaOHSFY/MzkuIbKhQmMlweQwPo1mknu3sGwBLI4cxt5e+XEEaxAXL3niOTfnxwXQm9aZTZDfTLlI9Bo8+xnW56J7ppEUpyQ6yCAjcwLloMXxGxfgMkHyd3GZ5pEDIP61w6n17xS4FrJfHzwch5KnRw4SviunyC0eGv/rNVsBsKSviuSrlR9slRIVWbj4zLgeekRTBHA0SLiXBkgt6rNzz3nI9gibStTww/fu8NqyZyXnBDApKtvlQRmCU3L3FmKiy4u2hFn3A23cVzQkmvbp8ctgigR4kGe8+m0hNj0PpU72mEk/XHi90nhSEdC0Q+H3iy1CyjzPOKxQ2DKfWB3+X9Oo82LoN+WlkpO6vyGkoPbbyVtZyb5O3Fl9Fbb9JSK4P/MlVVV25jPYLQEGpzo+Eheht8PtLebMlJ7uNqbBUy/Ii7OhAPD3Pk1ig2XP+4+4X8txP3OLsPsOCrRC5eQyfZpGLvsFRbw9bx6HKZX8q7yrFVfItpwcevbCm1C1GkK5kuLR4giO12CqgZH69ZzrQAqnilaUb2KCsGKQjiAwU21fbXVSpoQ6WL7OSZC3V/Xk889Y/2yPiHQ7kYV3/koN9uveFsor0RGP8FJlZuNTL65eJD5tDBXOLB4B5NPcCyLOc5/QZY2zDx4V37eqzKnTEq+d7UMvdRQ8xeTth17xj1CLZwEM+VItkOyeQNFEFNUB+BIcjQ4nZqMIIOmy7AEIs/1E8fhFEdJqiEdjkJH9pB4mStMIVjqmgen/XgwqLyM2koaXawa0PfEzCj6oWAAnteDX+RPbo3Idkn+n1bX0YFwDdr7DxBtYZJbarBiwByVT3+Txioy4LmUlj6hrwq99gFyHOUk6UtDZYMM8GVJf9gEAbofCkBXjuqo0ukWbZBFx+yj+nW53So07CX/TC89sWsOq9hh9zAX6Xh1W85Q6B+/hPpDMl1qU7KnfeJ0Qa6boVxT+SkWZXQvfxZptPxlO64O4hQWuKfjPWuLomkr3jZeGkPQnTwNbJyp2fSVUyvAsG1SzlIoVrbpKA5NTDe3fNk3iWbcUu/tzSrq1vng1SjxJCAV2ksd9XYCZ0gKJ97A1v9WTQgRaf2b8Ds9scqB1vw6P/xCfPVNvQSl+LAtbE8VmS53689ZiOqBqbNuitfL+5ti/eQi5NnnC61qAe/IHO/Lxi2JkJlmH6madpZFtvAqYXI9FWFTjpaw9VzRFAmDmoQWY3AZ2zHNcA6f4X7pXj19FhbQwBPN0pJ/Ee0v/nUQVLOL8PxCrOooKlLa3t70qTH4Q/ljfe5Vu4sQJ37pDaY4+nuNh+0llgPP14ntEaHMG+0TffJcuhRDeS+SGhBccEL2pgSyn7KVZKrksqgCGp3evqCEyEeiG486p9gSmPibzYqfC1JTEZ9uZttJDfc/2zWR4F0+lvgdUj1+1BcUufITY80w/dJhzy31a2urcsRL98kmyz331ua91AGpH9OYHVc+nabauni7pia95IqEiB+zuUWn3GLKCpPjqa4Pm6hijvkGqFa/r90cHCBIMCrMPFtgN+fQJjXC2xXt/vc5UD5E+/5qBzSGe97Vt82Uy+EqWnnx/C2PF5Ge1iknFzI1odvE3pQxtDRQvLxa4UBL1K8pjtpCicdIfL9Tii3v/eLmBbIBMHCFDDz23GgTc/GCfQ7DAt/QpcoHMSB3RHXaKRaIkYZcl1txL3FjgTwGLLBXjwU2yi4fY4EjJPT6JO/KCPBWVj7ICDzIaeq60pjJu4pBa4pC6VE3anzuvWq3O35rBC0/Bb06m8ACIaVYgEZtyf7vrqKuiKBnFQBKNWpjH7bp2TRoK/rmtms0UvnAbAAL0A0mnoiWDR7ZWaRMBIdtfiOAYqZtu4YYC/gXYt6+zoFoucF+lpRzYAEeUuD56hm33hyLjd4B14x0OHV1Gh882EfU7IzMmejxfCfXLFsarxXa1UkHSh/vFPJXPxbAgCaxwL63ABbgmPtAdIx2I94298tzJZhWXraR/W3BGV9NTGIni9ov34zfs9N1lre22DLEAm/8zbBAwYLpRUjWLReEPhYg/FWHBZRLavNs6v6RwxyazdWWMT2I76+f6et9HL4plJz3Ar6CKOOKXKeDCw1WO6A9ckT6sho/lKpWurNEVvfpiVB0OotuabhQSRCmcoNLArl+IYa71pnn9kWQcrbIrm//yKaKnrkb2ioHDJpzhQtz1ENGIE6ZVmfNx1OiiljAM0b3Zvlp59zGjwvQVuHNxue/U6uAwe1sVY/DyJEClMynZvwLkDSjOwFkJperQgc6Itn8m85YIH+AT3dX/uHtjWocFojQgJ2zJtaf1d2ESQvckN7DAptBwK2xjfTP7RQ68MQCzbnQlCksQIxWhW78deDOAt1wgJ1lLdLJP5iQNkaAr98UYwEk9To0JtFKRoN140YZC9Q7gOhfy9hcMLVbJF4SQ27u59x+fwzdcj2wvyG1uOLzE1+wuH5h/hr2Z2gPC3yOTVOrSMYCEGOnEPnxQSxgT40zUQrnsLTvu+F1gQUbBSXYRM1L3L/fMufb9jayL1n09K0yEyhptJmZGa7IjCBGt1eb3MBuCe1Tdp391Jtjn9ucdrfTGlKuJyscanx2XzPbVd6dFL2nwNh4IEqLvqvF1U9NLvzEzd0bTuDUr8b6umjltBHxqygfN5YPYlI/J+AqGy9goC2tChU9tDgfS1RhgoNLueXOJthwSxo2Xta2WoloN0rn1nyvLtKhfiyUc9ilvoDnu4mCO3WmrheSfWydb/A8uXbHe5jZJ94dlhZJvkIP4t5jDdyMLSwM0O1jxH/fMNNQzUuT2f55uFiDq05q+1CqZVSia00QoKkQ3aN/Yd9nrioTVgiFngupk0UkWqvBNC0jlvdrAhxXBegnoutTd+JZsMA5R8513kb1Zdc624z4BexFIwwqn/7WfQ2iAzOXvOrS7JZ2jxkC3VDxiR0vl3jBpLQfL+nG6sA2yuDkJz4NE9sYU7JUhAfPXtbPD0oHz6RYhYnl6pu7ykuwQI/c7aZiZdqfLvjY7XO4RykV5/4+ogn25GSi4cWWuYhDnDdhi4iyaG4oCiKR9X1kFS7y+ozljoQLjkIArB+effZt4rpnvYiV9cAecmDRBTm+8zbnja8ZtcmjTsiBngHTQI33j0thRvKo13o6sHXx7GBSafL9YlvpxB2NAe8zE75b8ULFCpNfcUtYBcHsLdZu91c9hOQsP/GcdQ9GKr+MBaI/9kp3uU+XOd3uecL27pXLqDW44rku88H5PPcVZ+g9lLxUx+YmLN/Cc/eUF9LLyp7OwHVQvcOJyxDa6xpO7t6irJCTM8GrdYcLdoZpwkNQcVhSoqc7CnuJy9dDhCiVyhoR+CCAtDD2l1qvY4T9DRVvLfqECXZzvz5/v6TJHc+jHymnKlmoV1Fp7wwH69RmjeRIqbTVddHFlJoTCxnXzgdPJbrlFXvb9ZrPy7sz7YDR7q+gJ/GyZzb6L3sDRm2uaCdhu8Tzgzj8uXEnIX5Io+R84RFGyRTC159oGjPspe59/62biSEGWDS+D6GWMTUuZ5pXxwel0VgAdCvAA7zkb9wToBv1BxDIrnnidYHKG592n8HOB0yjfK6q0xZazQbOge+cCxFvaW7VVQ97cDg54kpj4tLvx9WrW0kkjF93uW1+uSEv4950u7aiv/FtyG2+b13EBViYZJjdVxEosdKUamuiP9fyES5VZX7xrBaR9bsyPq87zzmAq+VAvOthxiHRs1dZzANIuCJlqF3BH1I/w3+yUH8DKau/Fuz6yn7WhcXF14vg1XImahDQ7OofBI6Zg3D0Ayx6vM23U53NixzeWQ46uiEYXCfDWpqRwZSzMEJQC83y1NORv7yui84DBfLr9VX0cf4pDflPeAOa1cNJcnQEa5oDH30uVduaWxyMipsj2dKa2JEGPw0TMr8mns9Kv0p8WfT44JsKRxRbbYpJcgI1D1N2KhwA7GnK/5Mj6f9PgGG//Q9QSwcIdT7kC6EnAAB4KgAAUEsDBBQACAgIADp4H0cAAAAAAAAAAAAAAAAWAAAAZ2VvZ2VicmFfamF2YXNjcmlwdC5qc0srzUsuyczPU0hPT/LP88zLLNHQVKiuBQBQSwcI1je9uRkAAAAXAAAAUEsDBBQACAgIADp4H0cAAAAAAAAAAAAAAAAXAAAAZ2VvZ2VicmFfZGVmYXVsdHMyZC54bWztml9T4zYQwJ/vPoXGT+0DieXESWAIN9zNdMoMx3UKc9NXxd44KrLkWjJx8ulPlvwvkNBgODLQvmCtIsmr3+5KK5nTT3nM0B2kkgo+dXDPdRDwQISUR1MnU/OjifPp7ONpBCKCWUrQXKQxUVPHL1rW/bTUw8NBUYdySU+4uCIxyIQEcB0sICaXIiDKNF0olZz0+8vlslcN2hNp1I8i1ctl6CCtEJdTpyyc6OE2Oi0Hprnnurj/19dLO/wR5VIRHoCDtLIhzEnGlNRFYBADV0itEpg6iWCrSHAHMTIDNnX+qOSyx9QZu87Zxw+njHK4VisGSC1ocMtBao08pxzGtYXfaRhCAc3pF33kQiyRmP0NgR5HpRnUrzGCaaN//iKYSFGqu/kDB2nIPnbQzAxKWLIgutQrR2RkBSm6I6z4tazRA34VIdjaoa0lnMaGLpIKkkIhJBOA0JRqlRM9nLHqnDBp9Dntl3i2gioYbJCyFQ0q/GqoXAPKfcDJPTSnecaDYsCr7ySt58AzxlqcRr7TZc6e7++Y9dg/9LQTQblq+YaW0C/zFODX1ryx22nebVsbBj/R2njbtD+cBkKkoUT51LkiVw5alc+1fZomhsA1XZevHLRrTTA0+j0RYwgJcB0saoMl7sRyNDEwi8fMPt4vTEZlw/LSCA2+wRZftDru44zYvR+ER/i11p5uC+x+RI/wk/3zW3uzxF4nr8SeXdnM8z8Z5Rf8T4joRuKBB/+z7MRy0yOH73jPMU0sK1n8nTqBiBMG+QsClhAVUs3rupJrxF63rejAKdxegLustCJTrHjXBVf6MAQmG5RW5dbLbwGSG935G79JCZfFIcq2qWA9tq+10vDLzRTce36K9Z5sAf/wjfCgOjpoQNW/ABZBJhvCVqoRT94oYpLllFGSrh744tPJPu/843Xb2Xavyd7Bzz8pWT22QnY78B3cZd7qClk54U4HfH5ScBB7vGSg3ulZiyZEv5dizWjbAektMPpJPrsl1SKpAkkJf5yzgrxJnm6M0LoQOSzkHTvC7sloo0SNchdWat1J2OnMqabESaw72BdR/pkEt1EqMh4+iPOXmfyrHb93wwkEp0Gt/Bcr1XCGbzSeOqVdNAJuFxiJUO6WnxFWrtUcrauaHJc1K1z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// is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View var views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 1,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0}; var applet = new GGBApplet(parameters, '5.0', views); window.onload = function() {applet.inject('ggbApplet')};

 
Alínea a)
:

Como os três triângulos são semelhantes, os comprimentos dos lados correspondentes são directamente proporcionais.…

0

Dois insectos

Decomposição de figuras - Teorema de Pitágoras: Matematicamente Falando 8 - Parte 1 Pág. 25 Ex. 14

Enunciado

Um insecto parte do ponto M e percorre os segmentos [MA] e [AC], parando no ponto C.

Um outro insecto parte do ponto C e percorre os segmentos [CB] e [BM], parando no ponto M.

  1. Prova que os triângulos [AMC] e [CMB] são semelhantes.
     
  2. Determina:
    – a distância que separa os dois insectos;
    – a distância percorrida pelo primeiro insecto.
Desenha um rectângulo [ABCD] 0

Desenha um rectângulo [ABCD]

Decomposição de figuras - Teorema de Pitágoras: Matematicamente Falando 8 - Parte 1 Pág. 25 Ex. 11

Enunciado

Desenha um rectângulo [ABCD] com $\overline{AD}=9\,cm$ e $\overline{BC}=5\,cm$.

Traça a diagonal [AC] e determina o baricentro do triângulo [ABC] e o baricentro do triângulo [ACD].

A que segmento peretencem os dois baricentros?

Resolução >> Resolução

Reproduz a construção e responde à questão.

var parameters = { "id": "ggbApplet", "width":713, "height":429, "showMenuBar":false, "showAlgebraInput":false, "showToolBar":false, "customToolBar":"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6", "showToolBarHelp":false, "showResetIcon":true, "enableLabelDrags":false, "enableShiftDragZoom":false, "enableRightClick":false, "errorDialogsActive":false, "useBrowserForJS":false, "preventFocus":false, "language":"pt", // use this instead of ggbBase64 to load a material from GeoGebraTube // "material_id":12345, "ggbBase64":"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// is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View var views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 1,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0}; var applet = new GGBApplet(parameters, '5.0', views); window.onload = function() {applet.inject('ggbApplet')};

 

 

<< Enunciado
0

A área da casa

Decomposição de figuras - Teorema de Pitágoras: Matematicamente Falando 8 - Parte 1 Pág. 24 Ex. 9

Enunciado

A Maria está a pensar comprar casa.

Numa imobiliária mostraram-lhe a planta ao lado.

Ajuda-a a determinar a área a casa.

Resolução >> Resolução

Considerando a planta da casa decomposta num quadrado, num tapézio e num triângulo, conclui-se que a área a casa é \[\begin{array}{*{35}{l}}
   {{A}_{Casa}} & = & {{A}_{1}}+{{A}_{2}}+{{A}_{3}}  \\
   {} & = & (10\times 10)+\left( \frac{12+8}{2}\times 2 \right)+(\frac{10\times 2}{2})  \\
   {} & = & 100+20+10  \\
   {} & = & 130\,\,{{m}^{2}}  \\
\end{array}\]
 

 

<< Enunciado
0

Calcula a área das figuras

Decomposição de figuras - Teorema de Pitágoras: Matematicamente Falando 8 - Parte 1 Pág. 24 Ex. 8

Enunciado

Calcula a área das figuras decompondo-as em triângulos e/ou quadriláteros, considerando as medidas indicadas expressas em centímetros.

 

Resolução >> Resolução

var parameters = { "id": "ggbApplet", "width":628, "height":155, "showMenuBar":false, "showAlgebraInput":false, "showToolBar":false, "customToolBar":"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6", "showToolBarHelp":false, "showResetIcon":true, "enableLabelDrags":false, "enableShiftDragZoom":false, "enableRightClick":false, "errorDialogsActive":false, "useBrowserForJS":false, "preventFocus":false, "language":"pt", // use this instead of ggbBase64 to load a material from GeoGebraTube // "material_id":12345, 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// is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View var views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 1,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0}; var applet = new GGBApplet(parameters, '5.0', views); window.onload = function() {applet.inject('ggbApplet')};

Na figura da alínea a), A1 é um quadrado, A2 um trapézio e A3 um rectângulo.…

1

Um telhado de quatro águas

Decomposição de figuras - Teorema de Pitágoras: Matematicamente Falando 8 - Parte 1 Pág. 24 Ex. 7

Enunciado

Há casas construídas com telhados de duas águas e outras com telhados de quatro águas.

Na figura está representado um telhado com quatro águas. Os números indicam as medidas em metros.


 Sabendo que para cobrir 1 m2 desse telhado são necessárias 15 telhas:

  1. quantas telhas, no mínimo, serão utilizadas para cobrir esse telhado, se na cobertura houver uma perda de 3%?
0

Os triângulos do Pedro

Decomposição de figuras - Teorema de Pitágoras: Matematicamente Falando 8 - Parte 1 Pág. 23 Ex. 3

Enunciado

O Pedro desenhou duas rectas paralelas.

Numa marcou os pontos C, D, E e F, na outra os pontos A e B, como mostra a figura.

Em seguida, uniu alguns pontos formando os triângulos [CAB], [DAB], [EAB] e [FAB].

Analisando esses triângulos, o Pedro descobriu um “segredo” sobre as suas áreas.…

0

[PQRS] é um paralelogramo

Do espaço ao plano: Matematicamente Falando 7 - Parte 2 Pág. 111 Ex. 6

Enunciado

[PQRS] é um paralelogramo.

  1. Quantos triângulos estão representados na figura?
     
  2. Calcula:   
  • $P\hat{Q}R$
     
  • $S\hat{T}R$
     
  • $P\hat{S}R$
     
  • $Q\hat{T}R$

Resolução >> Resolução

  1. Na figura estão representados 8 triângulos: [PQT], [QTR], [RTS], [STP], [PQR], [RPS], [RSQ] e [PQS].
     
  2. (Vai anotando na figura as amplitudes calculadas)
  • $P\hat{Q}R=180{}^\text{o}-(Q\hat{P}R+Q\hat{R}P)=180{}^\text{o}-(18{}^\text{o}+30{}^\text{o})=132{}^\text{o}$, pois a soma das amplitudes dos três ângulos internos de um triângulo é 180º.
A medida da amplitude do ângulo externo 0

A medida da amplitude do ângulo externo

Do espaço ao plano: Matematicamente Falando 7 - Parte 2 Pág. 103 Ex. 6

Enunciado

A medida da amplitude do ângulo externo em B, no triângulo [ABC], é 100º.

Sabendo que $\hat{B}=\hat{C}$:

  1. determina a medida da amplitude de cada um dos ângulos internos do triângulo;
  2. indica qual o lado de maior comprimento do triângulo e o de menor comprimento. Justifica.

Resolução >> Resolução

  1. var parameters = { "id": "ggbApplet", "width":278, "height":313, "showMenuBar":false, "showAlgebraInput":false, "showToolBar":false, "customToolBar":"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 6", "showToolBarHelp":false, "showResetIcon":true, "enableLabelDrags":false, "enableShiftDragZoom":false, "enableRightClick":false, "errorDialogsActive":false, "useBrowserForJS":false, "preventFocus":false, "language":"pt", // use this instead of ggbBase64 to load a material from GeoGebraTube // "material_id":12345, "ggbBase64":"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// is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View var views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 1,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0}; var applet = new GGBApplet(parameters, '5.0', views); window.onload = function() {applet.inject('ggbApplet')}; Como os ângulos ABC e CBD são suplementares, então $A\hat{B}C=180{}^\text{o}-C\hat{B}D=180{}^\text{o}-100{}^\text{o}=80{}^\text{o}$.