Veremos um exemplo de transposição didática por meio do Teorema de Pitágoras. Primeiramente, exploraremos a versão original que está no livro "Os Elementos" de Euclides. Vamos identificar fatores que podem dificultar a compreensão. Depois vamos analisar três exemplos de transposição didática, usando a plataforma GeoGebra e livros estáticos
[justify]Uma primeira dificuldade reside na compreensão da forma como foi escrito o teorema. [br]-Naquela época os lados dos triângulo não possuíam nomes específicos. [br]-Em [color=#0000ff]"[i]o quadrado sobre o lado ...é igual aos quadrados sobre os lados"[/i][/color] é preciso subentender que está tratando de áreas desses quadrados.[br]Analisemos agora a explicação/justificativa do teorema. [br]-Em [color=#0000ff]"[/color][i][color=#0000ff]Fiquem, pois, descritos, por um lado, o quadrado BDEC sobre a BC, e, por outro lado, os GB, HC sobre as BA, AC"[/color] . [/i]O quadrado BDEC está bem especificado pelos vértices. Já os quadrados ABFG e ACKH são chamados GB e HC. [br]- A parte [i][color=#0000ff]e, pelo A, fique traçada a AL paralela a qualquer uma das BD, CE; e fiquem ligadas as AD, FC[/color] [/i]foi usada para explicar e construir elementos novos na figura que inicialmente teria apenas um triângulo retângulo e três quadrados. [br]- A parte [i][color=#0000ff]E, como cada um dos ângulos sob BAC, BAG é reto, então, as duas retas AC, AG, não postas no mesmo lado, fazem relativamente a alguma reta a BA, e no ponto A sobre ela, os ângulos adjacentes iguais a dois retos; portanto, a CA está sobre uma reta com a AG[/color] [/i]é feita para mostrar que os segmentos estão sobre um mesma reta. A parte[i] [color=#0000ff]Pelas mesmas coisas, então, também a BA está sobre uma reta com a AH[/color] [/i]também é feita para mostrar que BA e AH estão sobre uma mesma reta. Isso era necessário?[br]- A parte [i][color=#0000ff]E, como o ângulo sob DBC é igual ao sob FBA; pois, cada um é reto; fique adicionado o sob ABC comum; portanto, o sob DBA todo é igual ao sob FBC[/color] [color=#0000ff]todo[/color] [/i]é feita para mostrar que os ângulos DBA e FBC são congruentes. [br]- Na parte [i][color=#0000ff]E como, por um lado, a DB é igual à BC, e, por outro lado, a FB, à BA, então, as duas DB, BA são iguais às duas FB, BC, [b]cada uma a cada uma[/b]; e o ângulo sob DBA é igual ao ângulo sob FBC; portanto, a base AD [é] igual à base FC, e o triângulo ABD é igual ao triângulo FBC[/color] [/i]O que quer dizer com [color=#0000ff][i]as duas DB, BA são iguais às duas FB, BC, cada uma a cada uma[/i]?[/color] Que DB=FB e BA=BC? Muito estranho porque a figura não mostra isso? Em [i][color=#0000ff]e o ângulo sob DBA é igual ao ângulo sob FBC; portanto, a base AD [é] igual à base FC, e o triângulo ABD é igual ao triângulo FBC[/color] [/i]está usando um critério de congruência para a afirmar que AD é igual FC e depois afirmar que ABD é congruente com FBC. Estranho. Os critérios de congruência já tinha sido explorados antes no livro? Se já tivesse sido, não bastaria apenas dizer que os triângulos são congruentes pelo critério LAL?[br]- A parte [i][color=#0000ff]por um lado, o paralelogramo BL [é] o dobro do triângulo ABD; pois, tanto têm a mesma base BD quanto estão nas mesmas paralelas BD, AL[/color]. [/i]Quem é o paralelogramo BL? Seria o BDLM na figura abaixo?[br][br][img]data:image/png;base64,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[/img][br]A parte [i][color=#0000ff]estão nas mesmas paralelas BD, AL[/color] [/i]é o mesmo que o segmento (altura) BM na figura acima. Ou seja, a área do triângulo ABD é igual [math]\frac{BD\cdot BM}{2}[/math] e do paralelogramo BDLM é [math]BD\cdot BM[/math][br]- A parte [i][color=#0000ff]por outro lado, o quadrado GB é o dobro do triângulo FBC; pois, de novo, tanto têm a mesma base FB quanto estão nas mesmas paralelas FB, GC [/color][/i]é semelhante a parte anterior. Ele quer mostrar que o quadrado ABFG (chamado de GB) é igual ao dobro do triângulo FBC, usando o fato de que ambos têm uma base comum (FB) e altura AB. Ou seja, a área do triângulo FBC é igual [math]\frac{FB\cdot BA}{2}[/math] e do quadrado ABFG é [math]FB\cdot BA[/math][br]- A parte [i][color=#0000ff][Mas os dobros das coisas iguais são iguais entre si;] portanto, também o paralelogramo BL é igual ao quadrado GB.[/color] [/i]é para mostrar que a área de BDLM é igual ABFG. É preciso lembrar que anteriormente foi provado que os triângulos ABD e FBC eram congruentes.[br]- A parte [i][color=#0000ff]Do mesmo modo, então, sendo ligadas as AE, BK, será provado também o paralelogramo CL igual ao quadrado HC;[/color] [/i]é feita para mostrar que o quadrado ACKH é igual ao retângulo CELM (figura acima). A ideia é a mesma do caso anterior. [br]- A parte [i][color=#0000ff]portanto, o quadrado BDEC todo é igual aos quadrados GB, HC. E, por um lado, o quadrado BDEC foi descrito sobre a BC, e, por outro lado, os GB, HC, sobre as BA, AC. Portanto, o quadrado sobre o lado BC é igual aos quadrados sobre os lados BA, AC[/color] [/i]é feita para concluir que BDLM (ABFG) mais CELM (ACKH) é igual a BDEC. [br][/justify]
Existem muitas maneiras de apresentar o teorema de Pitágoras. Vejamos um exemplo a seguir que foi retirado de um livro didático.
Quais são as dificuldades para compreender o Teorema de Pitágoras apresentado anteriormente?