199:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000 Pensamiento espacial:@0.721207:0.043660:0.914624:0.043660:0.914624:0.024915:0.721207:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Ejemplos 4:@0.073089:0.136836:0.156087:0.136836:0.156087:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a. Un triángulo tiene dos lados de longitud 6 cm y 4 cm, y el ángulo comprendido :@0.073089:0.160625:0.710187:0.160625:0.710187:0.144191:0.073089:0.144191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 entre ellos es de 60°. Otro triángulo tiene lados de 3 cm y 2 cm además, el ángulo :@0.103217:0.177267:0.710435:0.177267:0.710435:0.160833:0.103217:0.160833:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , :@0.566270:0.177267:0.572915:0.177267:0.572915:0.160861:0.566270:0.160861:0.000000:0.000000 :@0.633788:0.177267:0.637101:0.177267:0.637101:0.160861:0.633788:0.160861:0.000000 entre ellos dos es de 60°. ¿Son triángulos semejantes? ¿Cuál es la razón de semejanza? :@0.103217:0.193909:0.709905:0.193909:0.709905:0.177475:0.103217:0.177475:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Utilizando los postulados de semejanza de triángulos de la página anterior, podemos :@0.103217:0.218775:0.710566:0.218775:0.710566:0.202341:0.103217:0.202341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 conocer si los triángulos 1 y 2 son semejantes.:@0.103217:0.235416:0.436145:0.235416:0.436145:0.218983:0.103217:0.218983:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Aplicando el teorema LAL, tenemos: :@0.103217:0.272514:0.369181:0.272514:0.369181:0.256080:0.103217:0.256080:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.440747:0.272514:0.456762:0.272514:0.456762:0.256080:0.440747:0.256080:0.000000:0.000000:0.000000 :@0.531969:0.272514:0.536000:0.272514:0.536000:0.256080:0.531969:0.256080:0.000000 Reemplazamos los valores para encontrar la razón de semejanza::@0.103210:0.299877:0.571873:0.299877:0.571873:0.283443:0.103210:0.283443:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.073089:0.343834:0.077120:0.343834:0.077120:0.327400:0.073089:0.327400:0.000000 .:@0.315650:0.331227:0.318853:0.331227:0.318853:0.314793:0.315650:0.314793:0.000000 Conclusión::@0.103210:0.371197:0.192095:0.371197:0.192095:0.354528:0.103210:0.354528:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la razón de semejanza es 2, es decir, los lados correspondientes de los :@0.192025:0.371197:0.710736:0.371197:0.710736:0.354764:0.192025:0.354764:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dos triángulos son proporcionales y los ángulos y , ambos miden 60°. Por lo tanto, :@0.103210:0.387839:0.710454:0.387839:0.710454:0.371405:0.103210:0.371405:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A D:@0.445585:0.387839:0.481773:0.387839:0.481773:0.371433:0.445585:0.371433:0.000000:0.000000:0.000000 se cumple el teorema LAL. Los dos triángulos son semejantes.:@0.103210:0.404481:0.549913:0.404481:0.549913:0.388047:0.103210:0.388047:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 b. En la figura, dado :@0.073089:0.431844:0.232417:0.431844:0.232417:0.415410:0.073089:0.415410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.257677:0.433788:0.265040:0.433788:0.265040:0.415219:0.257677:0.415219:0.000000 AB DE:@0.236288:0.432027:0.286871:0.432027:0.286871:0.415621:0.236288:0.415621:0.000000:0.000000:0.000000:0.000000:0.000000 , demuestra: :@0.287706:0.431844:0.380350:0.431844:0.380350:0.415410:0.287706:0.415410:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ABC:@0.394564:0.432543:0.422819:0.432543:0.422819:0.417107:0.394564:0.417107:0.000000:0.000000:0.000000 EDC:@0.452086:0.432543:0.481538:0.432543:0.481538:0.417107:0.452086:0.417107:0.000000:0.000000:0.000000 .:@0.483635:0.431844:0.486838:0.431844:0.486838:0.415410:0.483635:0.415410:0.000000 :@0.073089:0.623501:0.104823:0.623501:0.104823:0.607068:0.073089:0.607068:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Demostración:@0.251116:0.471646:0.354916:0.471646:0.354916:0.456025:0.251116:0.456025:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Enunciados:@0.131269:0.498971:0.214387:0.498971:0.214387:0.483565:0.131269:0.483565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Razones:@0.340727:0.498971:0.400546:0.498971:0.400546:0.483565:0.340727:0.483565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. :@0.114681:0.527351:0.129424:0.527351:0.129424:0.512411:0.114681:0.512411:0.000000:0.000000:0.000000 :@0.154379:0.529737:0.161742:0.529737:0.161742:0.511168:0.154379:0.511168:0.000000 AB DE:@0.132990:0.527976:0.183573:0.527976:0.183573:0.511570:0.132990:0.511570:0.000000:0.000000:0.000000:0.000000:0.000000 2. :@0.114681:0.550044:0.129424:0.550044:0.129424:0.535104:0.114681:0.535104:0.000000:0.000000:0.000000 A:@0.143967:0.551205:0.153852:0.551205:0.153852:0.535770:0.143967:0.535770:0.000000 E:@0.183919:0.551205:0.192037:0.551205:0.192037:0.535770:0.183919:0.535770:0.000000 3. :@0.114681:0.572738:0.129424:0.572738:0.129424:0.557798:0.114681:0.557798:0.000000:0.000000:0.000000 1:@0.143131:0.574288:0.152113:0.574288:0.152113:0.558576:0.143131:0.558576:0.000000 2:@0.179945:0.574288:0.188928:0.574288:0.188928:0.558576:0.179945:0.558576:0.000000 4. :@0.114681:0.595431:0.129424:0.595431:0.129424:0.580491:0.114681:0.580491:0.000000:0.000000:0.000000 ABC:@0.141618:0.597040:0.169873:0.597040:0.169873:0.581604:0.141618:0.581604:0.000000:0.000000:0.000000 EDC:@0.199141:0.597040:0.228592:0.597040:0.228592:0.581604:0.199141:0.581604:0.000000:0.000000:0.000000 1. Dado.:@0.249926:0.524509:0.306861:0.524509:0.306861:0.509569:0.249926:0.509569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2. Si dos rectas paralelas se cortan :@0.249926:0.539638:0.477426:0.539638:0.477426:0.524698:0.249926:0.524698:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 por una transversal, los ángulos al-:@0.264157:0.554767:0.492606:0.554767:0.492606:0.539827:0.264157:0.539827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ternos internos son congruentes.:@0.264157:0.569896:0.483802:0.569896:0.483802:0.554956:0.264157:0.554956:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3. Los ángulos opuestos por el vér-:@0.249926:0.585025:0.479773:0.585025:0.479773:0.570085:0.249926:0.570085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tice son congruentes.:@0.264157:0.600154:0.407213:0.600154:0.407213:0.585214:0.264157:0.585214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4. Criterio AAA.:@0.249926:0.615283:0.348828:0.615283:0.348828:0.600343:0.249926:0.600343:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Conclusión::@0.103210:0.650865:0.191727:0.650865:0.191727:0.634195:0.103210:0.634195:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 los triángulos :@0.191601:0.650865:0.296810:0.650865:0.296810:0.634431:0.191601:0.634431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ABC:@0.311013:0.652055:0.339268:0.652055:0.339268:0.636619:0.311013:0.636619:0.000000:0.000000:0.000000 EDC:@0.368536:0.652055:0.397987:0.652055:0.397987:0.636619:0.368536:0.636619:0.000000:0.000000:0.000000 son semejantes.:@0.403652:0.650865:0.523450:0.650865:0.523450:0.634431:0.403652:0.634431:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 c. Un triángulo tiene como medidas de sus lados 18 , 12 y 9 , y otro triángulo :@0.073089:0.678228:0.710349:0.678228:0.710349:0.661794:0.073089:0.661794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.477510:0.678228:0.492125:0.678228:0.492125:0.661822:0.477510:0.661822:0.000000 m:@0.522773:0.678228:0.537389:0.678228:0.537389:0.661822:0.522773:0.661822:0.000000 m:@0.568571:0.678228:0.583186:0.678228:0.583186:0.661822:0.568571:0.661822:0.000000 tiene medidas 6 , 4 y 3 . ¿Cuál es la razón de semejanza? ¿Son semejantes estos :@0.103217:0.694870:0.710467:0.694870:0.710467:0.678436:0.103217:0.678436:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 m:@0.220931:0.694870:0.235547:0.694870:0.235547:0.678464:0.220931:0.678464:0.000000 m:@0.254230:0.694870:0.268845:0.694870:0.268845:0.678464:0.254230:0.678464:0.000000 m:@0.295904:0.694870:0.310519:0.694870:0.310519:0.678464:0.295904:0.678464:0.000000 triángulos?:@0.103198:0.711512:0.183134:0.711512:0.183134:0.695078:0.103198:0.695078:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Aplicamos el teorema LLL: :@0.103198:0.742951:0.301708:0.742951:0.301708:0.726517:0.103198:0.726517:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Reemplazamos los valores con cada lado :@0.103210:0.777619:0.444453:0.777619:0.444453:0.761185:0.103210:0.761185:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 correspondiente: :@0.103210:0.801573:0.230883:0.801573:0.230883:0.785139:0.103210:0.785139:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.073089:0.836084:0.077120:0.836084:0.077120:0.819651:0.073089:0.819651:0.000000 Conclusión::@0.103210:0.863448:0.191727:0.863448:0.191727:0.846778:0.103210:0.846778:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la razón de semejanza es 3. :@0.191601:0.863448:0.395445:0.863448:0.395445:0.847014:0.191601:0.847014:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Por lo tanto, los dos triángulos son semejantes.:@0.103210:0.890810:0.441502:0.890810:0.441502:0.874376:0.103210:0.874376:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A:@0.581493:0.482621:0.588241:0.482621:0.588241:0.471852:0.581493:0.471852:0.000000 B:@0.690466:0.482621:0.696632:0.482621:0.696632:0.471852:0.690466:0.471852:0.000000 C:@0.592340:0.544456:0.598934:0.544456:0.598934:0.533688:0.592340:0.533688:0.000000 D:@0.537497:0.579366:0.545184:0.579366:0.545184:0.568598:0.537497:0.568598:0.000000 E:@0.586602:0.579366:0.592186:0.579366:0.592186:0.568598:0.586602:0.568598:0.000000 2:@0.581481:0.551018:0.587576:0.551018:0.587576:0.540258:0.581481:0.540258:0.000000 1:@0.590926:0.532166:0.597021:0.532166:0.597021:0.521407:0.590926:0.521407:0.000000 A:@0.519060:0.887155:0.528517:0.887155:0.528517:0.872065:0.519060:0.872065:0.000000 E:@0.562481:0.815657:0.570306:0.815657:0.570306:0.800567:0.562481:0.800567:0.000000 18:@0.543051:0.852874:0.560133:0.852874:0.560133:0.837796:0.543051:0.837796:0.000000:0.000000 m:@0.560133:0.852874:0.576616:0.852874:0.576616:0.837784:0.560133:0.837784:0.000000:0.000000 12:@0.596328:0.891345:0.613410:0.891345:0.613410:0.876267:0.596328:0.876267:0.000000:0.000000 m:@0.613410:0.891345:0.629893:0.891345:0.629893:0.876255:0.613410:0.876255:0.000000:0.000000 9 :@0.681788:0.852874:0.693858:0.852874:0.693858:0.837796:0.681788:0.837796:0.000000:0.000000 m:@0.693858:0.852874:0.707311:0.852874:0.707311:0.837784:0.693858:0.837784:0.000000 3 :@0.573020:0.789316:0.585090:0.789316:0.585090:0.774238:0.573020:0.774238:0.000000:0.000000 m:@0.585090:0.789316:0.598543:0.789316:0.598543:0.774226:0.585090:0.774226:0.000000 6 :@0.490890:0.794333:0.502961:0.794333:0.502961:0.779256:0.490890:0.779256:0.000000:0.000000 m:@0.502961:0.794333:0.516413:0.794333:0.516413:0.779243:0.502961:0.779243:0.000000 4 :@0.506324:0.760052:0.518394:0.760052:0.518394:0.744974:0.506324:0.744974:0.000000:0.000000 m:@0.518394:0.760052:0.531847:0.760052:0.531847:0.744962:0.518394:0.744962:0.000000 D:@0.441775:0.768832:0.452547:0.768832:0.452547:0.753742:0.441775:0.753742:0.000000 F:@0.560866:0.760052:0.568608:0.760052:0.568608:0.744962:0.560866:0.744962:0.000000 B:@0.673330:0.803113:0.681971:0.803113:0.681971:0.788024:0.673330:0.788024:0.000000 C:@0.673330:0.893427:0.682570:0.893427:0.682570:0.878337:0.673330:0.878337:0.000000 A:@0.737426:0.213807:0.744614:0.213807:0.744614:0.201876:0.737426:0.201876:0.000000 D:@0.845767:0.213979:0.854148:0.213979:0.854148:0.202047:0.845767:0.202047:0.000000 C:@0.825834:0.213807:0.833036:0.213807:0.833036:0.201876:0.825834:0.201876:0.000000 F:@0.921726:0.213979:0.927576:0.213979:0.927576:0.202047:0.921726:0.202047:0.000000 3:@0.860145:0.193565:0.866678:0.193565:0.866678:0.181613:0.860145:0.181613:0.000000 6:@0.755578:0.180655:0.762111:0.180655:0.762111:0.168703:0.755578:0.168703:0.000000 1:@0.781789:0.193091:0.789861:0.193091:0.789861:0.179225:0.781789:0.179225:0.000000 2:@0.885284:0.201408:0.893357:0.201408:0.893357:0.187542:0.885284:0.187542:0.000000 60:@0.753537:0.206202:0.764153:0.206202:0.764153:0.196492:0.753537:0.196492:0.000000:0.000000 60:@0.863188:0.206407:0.873804:0.206407:0.873804:0.196696:0.863188:0.196696:0.000000:0.000000 B:@0.781006:0.147350:0.787431:0.147350:0.787431:0.135418:0.781006:0.135418:0.000000 E:@0.886375:0.168591:0.892279:0.168591:0.892279:0.156659:0.886375:0.156659:0.000000 4:@0.782348:0.218995:0.788881:0.218995:0.788881:0.207043:0.782348:0.207043:0.000000 2:@0.885032:0.218995:0.891565:0.218995:0.891565:0.207043:0.885032:0.207043:0.000000 Competencia :@0.740294:0.260470:0.848854:0.260470:0.848854:0.243523:0.740294:0.243523:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 matemática :@0.740294:0.277112:0.837769:0.277112:0.837769:0.260165:0.740294:0.260165:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Razón:@0.747016:0.297436:0.789528:0.297436:0.789528:0.282282:0.747016:0.282282:0.000000:0.000000:0.000000:0.000000:0.000000 Es el cociente entre :@0.747016:0.319712:0.878815:0.319712:0.878815:0.304772:0.747016:0.304772:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 dos números o dos :@0.747016:0.334841:0.877567:0.334841:0.877567:0.319901:0.747016:0.319901:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cantidades comparables :@0.747016:0.349970:0.912380:0.349970:0.912380:0.335030:0.747016:0.335030:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 entre sí, y se expresa :@0.747016:0.365099:0.884657:0.365099:0.884657:0.350159:0.747016:0.350159:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 como fracción.:@0.747016:0.380228:0.844909:0.380228:0.844909:0.365288:0.747016:0.365288:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Los términos de :@0.747016:0.451127:0.856184:0.451127:0.856184:0.436188:0.747016:0.436188:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 una razón se llaman :@0.747016:0.466256:0.882252:0.466256:0.882252:0.451316:0.747016:0.451316:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 antecedente y :@0.747016:0.481385:0.845598:0.481385:0.845598:0.466445:0.747016:0.466445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 consecuente. :@0.747016:0.496514:0.838988:0.496514:0.838988:0.481574:0.747016:0.481574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 El antecedente es :@0.747016:0.518792:0.867277:0.518792:0.867277:0.503852:0.747016:0.503852:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el dividendo y el :@0.747016:0.533920:0.859148:0.533920:0.859148:0.518981:0.747016:0.518981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 consecuente es el divisor.:@0.747016:0.549049:0.914559:0.549049:0.914559:0.534110:0.747016:0.534110:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Proporción:@0.747016:0.571327:0.823426:0.571327:0.823426:0.556173:0.747016:0.556173:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Proporción es una :@0.747016:0.593604:0.870159:0.593604:0.870159:0.578664:0.747016:0.578664:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 igualdad entre dos :@0.747016:0.608733:0.874672:0.608733:0.874672:0.593793:0.747016:0.593793:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 razones.:@0.747016:0.623862:0.800634:0.623862:0.800634:0.608922:0.747016:0.608922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Constante de :@0.747016:0.692366:0.842454:0.692366:0.842454:0.677212:0.747016:0.677212:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 proporcionalidad o :@0.747016:0.707495:0.882937:0.707495:0.882937:0.692341:0.747016:0.692341:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 razón de semejanza:@0.747016:0.722624:0.883758:0.722624:0.883758:0.707470:0.747016:0.707470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Es el cociente entre :@0.747016:0.744901:0.878815:0.744901:0.878815:0.729961:0.747016:0.729961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el antecedente y :@0.747016:0.760030:0.860726:0.760030:0.860726:0.745090:0.747016:0.745090:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 el consecuente de :@0.747016:0.775159:0.872128:0.775159:0.872128:0.760219:0.747016:0.760219:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 cualquier razón de una :@0.747016:0.790288:0.901950:0.790288:0.901950:0.775348:0.747016:0.775348:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 proporción.:@0.747016:0.805417:0.823861:0.805417:0.823861:0.790477:0.747016:0.790477:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DBA 6 (Ev. 4) Redacta y argumenta procesos llevados a cabo para resolver situaciones de semejanza y congruencia de figuras.:@0.084956:0.971366:0.743605:0.971366:0.743605:0.959415:0.084956:0.959415:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 MUESTRA EDITORIAL:@0.248902:0.947499:0.888171:0.113285:0.743922:0.050540:0.104653:0.884754:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Muestra editorial solo para fines didácticos – Prohibida su venta:@0.095585:0.659700:0.095585:0.341447:0.077558:0.341447:0.077558:0.659700:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000