[b]Soma [/b]das amplitudes dos [b]ângulos internos[/b] e [b]soma[/b] das [b]amplitudes dos ângulos externos[/b] de um triângulo no GeoGebra [br][br]O [b]objetivo [/b]da tarefa é efetuar construções que te ajudem a estabelecer uma conjetura quanto às [b]somas [/b]das amplitudes dos [b]ângulos internos[/b] e dos [b]ângulos externos[/b] de um triângulo.
[size=200][color=#ff0000]Ângulos Internos[/color][/size]
[size=150][b]Constrói [/b]um triângulo qualquer, [[i]ABC[/i]] : Seleciona a ferramenta “[i]Polígono [img]data:image/png;base64,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[/img][/i]” e clica sequencialmente[br]em [b]três pontos[/b] que vão corresponder aos [b]vértices [/b]do triângulo e termina clicando no [b]vértice [/b]inicial.[br][br]Para mostrares os rótulos dos vértices, seleciona “[b]Mostrar/Esconder Rótulo [img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACEAAAAgCAYAAACcuBHKAAAEk0lEQVRYR+2Xa0xbZRjH/6eXcWk7xiV2dOKgdMMNDGyryoiIm7sBMzFbNi8xcUtkmMkHMy98mImZoHMxKkxm4i6RmJhlXuMljkVBF2/IrcCYC1HjQDqxlEKhN1pKfd5zenqRxrRg55e9ScNpec95f+//eZ7/+xzORwP/8+BCIRiPy+2FY8aLeJHJpRKokmSQSLjA1sMgvrlkwulvr8I5OwcubhhASXYqDmzVQUkwbPAQTAEG8InhT+y/eyU0ackEEZ/hIKU/7jRi0unBc/evgVTKCRB21ywOnxvAfUXLcW/h8visHvLUaYcHtWf78fyufKhTEwWICZsbVc0GHNudj9xMZdwh2AL1H/yMyqJMrNOlBiEea+7BK7sLoL1OEC8RxHZSfcOqtBsQi1fC56My5iQLzp//IBw+MJ/luPmFzMqd/Sz8FSAZMM0Omx8TBO/qworscfwlbzD0nX2EBcTfJPzivjlSSSLxLyp6bzhwDBDsAeLNPkxNWtHV0c72BH1xMZSqpYFdCzsFrDTHPGZCeno6li6j8vPD/zN0UUMIZ1twJ19+8Tleb2iAVCJFXX09Cjfo6QwI5oXH40ZvVxd6DAbcmpeH24s3IlmhiJg3sUH4QzFttaKp4TX0DwxgzGxGxfYdqK6pgUKp8ofFh3GTCT/+8D3sDgevX2lZGTJX3Bwxd2KDEFILF1u/QmNjIzaV3YNh4wiGh4Zw9OjL0K7OC+TGlcuX8cvgINasXYu+3l5oNJm4o+QuyOXyeWrEAMHKkIPL6cSZk2+hpeUCap+thd1uw4k3T2DPnr14ZN9+fo57xoWLbV9DJpehuGQjDJ2dGDFeQ3lFJZQpKfPUiAoimA8cfh28gheOHIGDZH7ogQfhIKhz778HdUYGXj3+BlIoAccpGS+cP4+srCxk5+TATKHp678EvX498guL6LQUjm1xRAUh1LcPc14vPvvoQxxvaoI2JxsKRTKfq+bxcVgmJvHEwYPYVlGBzvZ2DFGI1Go15DIZvHTfuMUCGV1v3VFOuRN+MEYNwUBcTgcO1wohOPT0MyS3EN+RP4Zx6uQp5Gq1OFBdjbbWVsoFOoVX6WjXUvIKH/4aHUV3dxfupHLO0elCyh2IGoKpMHrNiDoKRWlpKR5+dF9ATpYn75w5DYOhBzsrd8Lp9mDzli1IJX8Qzc02PYXujp+wjMJ1W9E6SEmVBYWDyWqhklSqVEhKTgqxYh/sNhsc9GH/46hnTEhMJN+QCvXEnJPcdJbgmHsyBUNtPmolwusqsv2Kc4QDjbmD4LBiEy86pjAvaN0LhAhHWuy3GxAxJ+ZiJf+3+yOGo4oa3WO7CpCruT7d9ovU6JZTo7tebHSn6D3g0Lt9eHyTFnpdWjwFCFTOk829eKpyNW65SSF023Pkbp92GNFxdQJVZdnIUC3ha1vopqIf4nnDt3Z8Rfrv5/sS4XrG40VLvwkDI1bU7S0gi6cOTHwhZje+3fY7vvvNghWqhIg9QFQ4gVZw/my2hpXe9pbIJaihd9GValKB4YW+lTNFxqwumCZnAmYT1cIxTFImyqHJSEICgYgO+jej3Pq/ourRbwAAAABJRU5ErkJggg==[/img][/b]” e clica nos pontos.[/size]
[size=150][b]Assinala [/b]as amplitudes dos [b]ângulos internos[/b]: Seleciona a ferramenta “[b]Ângulo [img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAACAAAAAeCAYAAABNChwpAAAIIUlEQVRIS8VXaUxc5xU9b94sDAGzGMOweBgwYBc7xaWOjGuTqI0au0mcFrI1oq2XRm0qteqWKlJ/VGok25VbJVLVNlWVhdhJ26R2mriqVZtIVJaQo+DY2NjG2OAUMFvYBphhmO1Nz/3eexhhUH5VfcPALN/77vnOPffci5bihf/jpS0GMB9LoL17CgOTc/hfwcr0OrGlIheFuWnQNA0LAEKRBA6duAYjmcKG4kw4NCGGC/gAUuoBOG5zZSPkJnKZb1NqtbrUC/5KGfxjr0lhajaOS8Mz2Le9FNs/k2cCiCcM/PF0L2838O0vlsHrcfKLJDSHBJSncRuAxvcSzQKgYNpRFz4mEHWvLCN0fq7W8EXCMNBxcxqvtvXjhaYaE8B0OIbvH+3Aczv9qPbn8mYnFxOAuktfxADfCwC1swHupTbWBJ6RRGguitmZWXi9XqzKSofukMhuE4AAMuJqX9nz52914Vv1ARPAVCiGp5vP49cN61BWmMUFBIAEN5fgEtBMgEmtDUBOJp+atEejUbxx5B/48NwFrC0pQmPDA6jexAACQAGWXwnFpuxx8PgN7KopXAKgsRxlvmwusBmwU3AngJQcnwA0LYkkD9XW1o5Dh45hZCJCHUXwxCN1+MGPn0JW5ipTCiq4HIA/ZO/AO73LAaggAN7gcBMod7WFZJ9+ccGa2uSaJGLzcbz0UjPefvcq5qMORCNT+NKOSvzsuT3wr/VbpyZgtaE8EzigGChaykAlUyCIXVxG4ZkMW0BsGu1UWO+Z0wQr58SJFrz4wnsYmwip0+5t+jJ+9NMmpKd5LKGYubcBHDx+HTvvTEEVygqEAVN46rIALChdPrLULp8lEwlc6byII683w++vgZFyorKyHBuZ/0Agn/FMAKIXVfeKgSQ10P1pAIQyiaaSptSekteLQMmmXZ1XcPzYW1idl41HH2uCJ82L9Iy74HIavEfK18O/tn+IYM0UfAoDZu2bF9lQpbPYiMwTDfynD0dffwNOl449+/agwEdVC1JVn1zP0rOtySxpG0BcVcHyKRARKrMR1crppSQJwFDFbBLA16PDQzj68stYU7QWux5+iMHzFwVnYDEgghBHTaUcxMOzixcIsFQMB9/pIYDlRKgA6AwSYyje6HCZAJQkBBgw1N+Hv7zyJ7gI6PF9++HzU+kqvzSnWAyJSBQOp07sOhweYZCvCQI6/yoi5gng5nIAKEJfJg/rIItz3FDnPWmMb1qx7DE9MYnm3/0BaR8PoCwrA1uaHsWq6s8i7kmHm81s+soljJ9ugTtvDVZtrEbO1lrALTogmAURrpQCcUJhgIGTRCkp0B0EIPQTwMjQMN5ubkZ0cgoP126Fa2YaUzMjqN69G3rVRkQGR9D9fgsC6em4fOEcirfVoYLpge4idw7uZaVhJRH+pmEtAvk5yr+hUQNELC4n+ZwY/QR/+/NfMdh9HY331aPMvw4IhxFsfR/uDQGUfHM/pvsG0dXairtrNuDiv05idUUFAo1PML4HTu6h69STLjpaiYGv+VHuyyHVHgqfdIai+KjjJpKRMHoufYRrZ/+NB++/H3WklueBg6kZaD+DEGK4e+9eJD3ZuHW+HbOd7YDHi9yqahTX7YCTjEjqHRShRhaUCI+LCJf2ggb2gsJsZSbjo6N45bV38c/Wq0BkDN7UHJ59fBc+X70eXlEzhSVpmRnsxa3RIRTdtwN5m7ciHiGcvm6k5RXCmbkaelo6BcmqoGDtzik+cEhVwR3NiJT5sqhlHe0fnsfzh9/ExyN3wZMYR0Z8Aj98pAZbNq1ng8kgrV5lKtFb/RjsH0Du1ntQXH8vQE9wsIIMlq8hVaSEJ+VotWTl7ysAONxIALTiFG/uvHgZhw4fRVdvDJoRRKYjhK9sykGhL0951OrcAgRKSpAzH8bQwAB827ahpL4euls6qUERUz/iRYp6PgWA+IgyVvGB3uUYWEcAWQpANDyD1lNtOHVK8qlRWBWo316Lvp4b6LpwEYkYBxbWvOeTfsSo1LqdD6KK+vCQHS8HmhCnrPGpIIZYrsVFPpSU+uB2i7hlDoxaAJYaUYOfKchVVSAjmQQZHppkd3YiLz8LLhdNiRQm56OYZCn29fZg+tZ1jI0HMTAyg2BkEkVkZfPmOnR29+HM2Q7MThrYWFWOZ773VZRXiWGJK9oAlmhAytCfn8tmSKTCs8qXiE0oZR7ZJdV4Jd6oOiIbDv1ibi6G4eExjPT3IhwKo+3seZz54CqC85wtNR/WZLux/+vb8NSex6BTkLRLy4rvqIKy2xMRa9VsJJwNxAzEg3UpIUpK0WgNhGKP0m7lezYhGWxnZ8fw7E9+j7PnBoCsAuSmJfD0k3Vo2kcA9AEtRR9YtgpYhkoD3NThiKnSoY+a/UMecmJ5SD1LQPWjplJralRzPhLxCF579SROnv4A4aQLtRtK8d3v7EagvFj5wMoAGtkL8jPMpqPRilXteq3g3JjmJCToC+O62R0NmZDZsDQxXAFNg5oMzqLzyjVMByNYv54HKyuAmxpS4MnAATKwMJQGORU/c6QDv3ioBFXFNA92QE1jCqSNyoSsRjmZAUQX8nLxbGCf3hoZ1FJzXjBnSrnUNKOewpxBH3j+2A003lNizoTReBK/+vs1VPjcePILfguA3YIpQtPCrJYsGyoU5saLLjUpW/Hsic5cYq3j9wafg5Nh/PK9G3jxG5tNAIL25lAIv23pQW0gG5UFdDr5p2JJIJVvezK2QS1GwK55+2tLG/zMxMqzM3iQ/wS1XB7D50qz0XRvKf4LfJFj2qB0zdAAAAAASUVORK5CYII=[/img][/b]” e clica no interior do triângulo.[/size]
Com a ferramenta “[b]Mover[/b] [img]data:image/png;base64,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[/img]” selecionada, obtém diferentes triângulos (quanto aos lados e quanto ao[br] ângulos) e, com a ajuda da máquina calculadora, [b]obtém a soma das amplitudes dos três ângulos[br]internos de cada triângulo. [/b]
Que [b]conjetura [/b]efetuas quanto à [b]soma das amplitudes dos ângulos internos[/b] de um triângulo? [br][b]Regista [/b]a tua conclusão.