Para iniciar o tema temos um desafio![br][br]Na janela do geogebra encontras um triângulo retângulo e sobre cada um dos seus lados foi desenhado um quadrado.[br]1. Com todas as peças coloridas tenta preencher os dois quadrados menores;[br]2. Agora com essas mesmas peças tenta preencher o quadrado maior.

Agora é a tua vez![br]1) Na janela do Geogebra constrói um triângulo ABC retângulo em A, para isso segue os passos seguintes:[br][list][*]Constrói um segmento de reta AB;(Clica em [img]data:image/png;base64,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[/img]e marca os pontos A e B)[br][/*][*]Constrói uma reta perpendicular a [AB] que passe por A (Clica em [img]data:image/png;base64,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[/img] e seleciona o ponto A e o segmento [AB]; [/*][/list][list][*]Marca um ponto C na reta que acabaste de desenhar (Seleciona [img]data:image/png;base64,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[/img] e marca um ponto C[br] na reta perpendicular;[br][/*][*]Constrói o triângulo usando [img]data:image/png;base64,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[/img]e selecionando os pontos A, B e C (no fim clica novamente em A para fechar o triângulo); [br][/*][*]Esconde agora a reta perpendicular usando [img]data:image/png;base64,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[/img] [/*][/list]

2) Constrói um quadrado sobre cada um dos lados do triângulo, para isso segue os passos:[list][*]Clica em [img]data:image/png;base64,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[/img] e seleciona os pontos B e A (a ordem é importante). Abre-se uma janela. Escreve “4” e carrega OK; [br][/*][*]Procede do mesmo modo para os segmentos [BC] e [CA]. [br][/*][/list]3)Considera o triângulo que construístes e os respetivos quadrados construídos sobre cada um dos seus lados. [br]Usando a ferramenta [img]data:image/png;base64,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[/img], determina a área de cada um dos três quadrados e [b][color=#0000ff]completa a tabela 1 que se encontra no [b][color=#0000ff]teu [/color][/b]percurso de aprendizagem: [/color][/b]

Na tua construção desloca os pontos A, B e C, obtendo assim novos triângulos e volta ao teu [b][color=#0000ff]percurso de aprendizagem e [/color][/b][b][color=#0000ff]completa a tabela 2.[/color][/b]

Visualiza o vídeo.