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Consideremos dos rectas coplanares r y r’

Teorema de Thales. Consideremos dos rectas coplanares r y r’. r. r’. Teorema de Thales. Sean a, b, c y d rectas paralelas. a. b. c. d. r’. r. Teorema de Thales. a. A’. b. Consideremos:. A. B’. B. c. C’. d. D’. C. r’. D. r. AB. A’B’. CD. C’D’. Teorema de Thales.

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Consideremos dos rectas coplanares r y r’

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  1. Teorema de Thales Consideremos dos rectas coplanares r y r’ r r’

  2. Teorema de Thales Sean a, b, c y d rectas paralelas a b c d r’ r

  3. Teorema de Thales a A’ b Consideremos: A B’ B c C’ d D’ C r’ D r

  4. AB A’B’ CD C’D’ Teorema de Thales a A’ Entonces se cumple que: A b B’ = B c C’ d D’ C r’ D r

  5. A(AB’C) A(ABC’) A(AB’C’) A(AB’C’) AC.h2.0,5 AB.h1.0,5 AC’.h2.0,5 AB’.h1.0,5 AC AB AC’ AB’ r Caso particular tienen igual área y (B’C’C) Los triángulos: (B’C’B) = Entonces tenemos que: En consecuencia: = Cancelando: A h2 h1 B’ = C’ B C

  6. = = AC BC AB B’C’ AC’ AB’ Teorema de Thales en triángulos Tesis: Hipóesis: • (ABC) • B’Î AB, C’Î AC • con B’C’//BC A B’ C’ B C

  7. JC=B’C’ = = BC BC AB AB B’C’ AB’ AB’ JC r Teorema de Thales en triángulos Demostración: Consideremos r paralela a AC por B’, que corta a BC en J Como B’J//AC Þ (*) Por lo demostrado en el caso particular Como (B’C’CJ) es un paralelogramo Þ (**) A De (*) y (**) se desprende: B’ C’ B J C

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