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Considérons un triangle ABC I le milieu du segment [AB] J le milieu du segment [AC]

Considérons un triangle ABC I le milieu du segment [AB] J le milieu du segment [AC]. On conjecture que (IJ) // (BC). Astuce : Placer le point K: le symétrique du point I par rapport au point J. Quelle conjecture peut-on faire sur le quadrilatère AICK ?. AICK est un parallélogramme.

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Considérons un triangle ABC I le milieu du segment [AB] J le milieu du segment [AC]

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  1. Considérons un triangle ABC I le milieu du segment [AB]J le milieu du segment [AC]

  2. On conjecture que (IJ) // (BC)

  3. Astuce : Placer le point K: le symétrique du point I par rapport au point J .

  4. Quelle conjecture peut-on faire sur le quadrilatère AICK ? AICK est un parallélogramme

  5. Démontrons le ! Voir page 27-28 de la boite à outil pour le choix de la propriété : utilise le codage !!

  6. Démontrons le !

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