Teorema di Pitagora: storia di una semplice dimostrazione

Si dice che Pitagora ebbe l’intuizione del suo famoso teorema mentre era seduto in una grande sala con[br]una pavimentazione di pietre quadrate.
A cosa serve il Teorema di Pitagora nella vita di ogni giorno? Come si calcola la lunghezza dell'ipotenusa di un triangolo rettangolo? Come si calcola la lunghezza del cateto? Scopriamolo insieme guardando questo video tratto da www.schooltoon.com

Schede studente per attività sul teorema di Pitagora

Schede studente Pitagora

Verifica

Marco vuole installare dei pannelli solari sul tetto del suo box auto. La superficie su cui poggeranno i pannelli deve essere inclinata per ricevere i raggi del sole nel modo più efficace. Il progetto di Marco è schematizzato nella figura. La superfici
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[/img]
Mauro ha il banco attaccato al muro dell’aula. Appoggia un righello di 10 cm verticalmente. Poco dopo il righello scivola di 2 cm, come in figura. Di quanti cm il piede del righello si è allontanato dal muro?
[img]data:image/png;base64,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[/img]

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