Theoreme de thales cours fr

Chapitre4ThalsI Homothties1. DfinitionsDfinitionSoit O un point nomm centre et k un nombre nomm rapport. Si A est un point,alors limage de A par lhomothtiede centre O et de rapport k est :le point A [O A) tel que O A = k O A si k > 0,le point A [AO ) tel que O A = k O A si k < 0.Exemple 1 (rapport positif) : On a dabord trac le triangleABC bleu et choisi un point O , puis on a trac son image parhomothtie de centre O et de rapport 3. On a ainsi obtenu letriangle A B C rouge :CExemple 2 (rapport ngatif) : Repartons du triangle ABCbleu et du point O , mais traons cette fois-ci son image parlhomothtie de centre O et de rapport 2. On obtient alorsle triangle A B C vert :CBBAObbbACbA bbBAB C O Comme lhomothtie est de rapport > 0, la figure obtenueest dans le mme sens que celle dorigine. Comme lhomothtie est de rapport < 0, la figure obtenueest dans le sens contraire que celle dorigine. Les distances O A , O B et O C ont t multiplies par 3pour obtenir les distances O A , O B et O C . Les distances O A , O B et O C ont t multiplies par 2 (eneffet, la dfinition parle de k = (2) = 2 !) pour obtenirles distances O A , O B et O C .Dfinitions Si la valeur numrique du rapport est infr ...


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