Teorema di Talete

Il [i]Teorema di Talete[/i] relativo a un fascio di rette parallele tagliate da due trasversali, garantisce che le lunghezze dei segmenti compresi tra due rette parallele che si formano sulla prima trasversale sono direttamente proporzionali alle lunghezze dei segmenti compresi tra la stessa coppia di parallele sull'altra trasversale.[br][br]Formalmente:[br]Ipotesi: [math]a\parallel b\parallel c\parallel d[/math][br]Tesi: [math]\overline{AB}:\overline{A'B'}=\overline{BC}:\overline{B'C'}[/math].[br]La stessa proporzione vale per qualsiasi coppia di segmenti corrispondenti individuati sulle due trasversali.[br][br][br]Esplora il Teorema di Talete nell'app che segue, poi svolgi le attività indicate di seguito.
Ora tocca a te...
Nell'app qui sopra, utilizza i pulsanti e visualizza solo le misure della prima coppia di segmenti, [math]AB[/math] e [math]A'B'[/math].[br]Muovi le parallele e le trasversali in modo da ottenere che il rapporto tra le misure di [math]AB[/math] e [math]A'B'[/math] sia uguale a [math]1[/math].[br][br]Cosa puoi dire sulle lunghezze dei due segmenti?[br][br]Come descriveresti la posizione reciproca delle due trasversali?[br][br]Esiste solo una posizione reciproca delle due trasversali affinché la proprietà metrica che hai mostrato sia valida?
Ora visualizza le lunghezze di tutte le coppie di segmenti.[br]Muovi le parallele e le trasversali in modo che il rapporto tra le lunghezze di [math]AB[/math] e [math]A'B'[/math] sia uguale a 1.[br][br]Cosa puoi dire relativamente alla lunghezza di tutte le coppie di segmenti corrispondenti visualizzate?
Facendo riferimento al grafico nell'app, scegli quale delle seguenti proporzioni è vera.
Possiamo dire che per il teorema di Talete vale anche [math]\overline{AB}:\overline{A'B'}=\overline{AC}:\overline{A'C'}[/math]? [br]Spiega il motivo della tua risposta.
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[/img][br]Considera sui lati [math]AB[/math] e [math]CD[/math] del parallelogramma [math]ABCD[/math] due segmenti congruenti [math]BE[/math] e [math]DF[/math].[br]Unisci [math]D[/math] con [math]E[/math] e [math]B[/math] con [math]F[/math], e siano [math]G[/math] e [math]H[/math] rispettivamente i punti di intersezione di [math]DE[/math] e [math]BF[/math] con la diagonale [math]AC[/math] del parallelogramma.[br][br]Dimostra che [math]AG\cong HC[/math].
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Information: Teorema di Talete