197:@0.942817:0.963886:0.974741:0.963886:0.974741:0.945448:0.942817:0.945448:0.000000:0.000000:0.000000
Ejemplos:@0.095800:0.126195:0.159794:0.126195:0.159794:0.111083:0.095800:0.111083:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a):@0.095800:0.150235:0.111316:0.150235:0.111316:0.133099:0.095800:0.133099:0.000000:0.000000
  Un triángulo tiene dos lados de longitud 6 :@0.111316:0.150235:0.440029:0.150235:0.440029:0.134565:0.111316:0.134565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.440232:0.150235:0.462529:0.150235:0.462529:0.133874:0.440232:0.133874:0.000000:0.000000
 y 4 :@0.462529:0.150235:0.492143:0.150235:0.492143:0.134565:0.462529:0.134565:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.492345:0.150235:0.514643:0.150235:0.514643:0.133874:0.492345:0.133874:0.000000:0.000000
, y el ángulo comprendi-:@0.514643:0.150235:0.694220:0.150235:0.694220:0.134565:0.514643:0.134565:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
do entre ellos es de 60°. Otro triángulo tiene lados de 3 :@0.124290:0.166831:0.535262:0.166831:0.535262:0.151162:0.124290:0.151162:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cm:@0.535685:0.166831:0.557983:0.166831:0.557983:0.150470:0.535685:0.150470:0.000000:0.000000
 y 2 :@0.557983:0.166831:0.588038:0.166831:0.588038:0.151162:0.557983:0.151162:0.000000:0.000000:0.000000:0.000000:0.000000
cm, además, :@0.588462:0.166831:0.680840:0.166831:0.680840:0.150470:0.588462:0.150470:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el :@0.681190:0.166831:0.698070:0.166831:0.698070:0.151162:0.681190:0.151162:0.000000:0.000000:0.000000
ángulo entre ellos dos es de 60°. ¿Son triángulos semejantes? ¿Cuál es la razón :@0.124290:0.183428:0.698177:0.183428:0.698177:0.167758:0.124290:0.167758:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de semejanza? :@0.124290:0.200024:0.236164:0.200024:0.236164:0.184354:0.124290:0.184354:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.095800:0.223743:0.099836:0.223743:0.099836:0.208073:0.095800:0.208073:0.000000
Utilizando los postulados de semejanza de triángulos de la página anterior, :@0.124290:0.223743:0.698164:0.223743:0.698164:0.208073:0.124290:0.208073:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
podemos conocer si los triángulos 1 y 2 son semejantes.:@0.124290:0.240339:0.535735:0.240339:0.535735:0.224670:0.124290:0.224670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.095800:0.273781:0.099836:0.273781:0.099836:0.258111:0.095800:0.258111:0.000000
Aplicando el teorema LAL, tenemos: :@0.124290:0.273781:0.393074:0.273781:0.393074:0.258111:0.124290:0.258111:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.422756:0.273547:0.432873:0.273547:0.432873:0.257974:0.422756:0.257974:0.000000
AB:@0.398892:0.263907:0.417320:0.263907:0.417320:0.247546:0.398892:0.247546:0.000000:0.000000
DE:@0.397157:0.283360:0.416800:0.283360:0.416800:0.266999:0.397157:0.266999:0.000000:0.000000
AC:@0.439090:0.263911:0.458586:0.263911:0.458586:0.247550:0.439090:0.247550:0.000000:0.000000
DF:@0.438357:0.283360:0.457928:0.283360:0.457928:0.266999:0.438357:0.266999:0.000000:0.000000
 y :@0.465109:0.273780:0.481289:0.273780:0.481289:0.258110:0.465109:0.258110:0.000000:0.000000:0.000000
A:@0.497080:0.275037:0.506975:0.275037:0.511771:0.258676:0.501876:0.258676:0.000000
D:@0.538173:0.275037:0.549709:0.275037:0.554505:0.258676:0.542969:0.258676:0.000000
:@0.484272:0.275908:0.457331:0.275908:0.457331:0.259160:0.484272:0.259160:0.000000
:@0.525366:0.275908:0.498425:0.275908:0.498425:0.259160:0.525366:0.259160:0.000000
=:@0.511914:0.275715:0.522031:0.275715:0.522031:0.260142:0.511914:0.260142:0.000000
 :@0.556673:0.273780:0.560709:0.273780:0.560709:0.258110:0.556673:0.258110:0.000000
 :@0.095798:0.297499:0.099834:0.297499:0.099834:0.281829:0.095798:0.281829:0.000000
Reemplazamos los valores para encontrar la razón de semejanza::@0.124287:0.297499:0.597982:0.297499:0.597982:0.281829:0.124287:0.281829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.095798:0.343858:0.099834:0.343858:0.099834:0.328188:0.095798:0.328188:0.000000
=:@0.153975:0.330708:0.164092:0.330708:0.164092:0.315135:0.153975:0.315135:0.000000
→:@0.196175:0.330708:0.214363:0.330708:0.214363:0.315135:0.196175:0.315135:0.000000
=:@0.233864:0.330708:0.243981:0.330708:0.243981:0.315135:0.233864:0.315135:0.000000
=:@0.281039:0.330708:0.291156:0.330708:0.291156:0.315135:0.281039:0.315135:0.000000
AB:@0.130098:0.321068:0.148526:0.321068:0.148526:0.304707:0.130098:0.304707:0.000000:0.000000
DE:@0.128366:0.340514:0.148010:0.340514:0.148010:0.324152:0.128366:0.324152:0.000000:0.000000
AC:@0.170307:0.321068:0.189804:0.321068:0.189804:0.304707:0.170307:0.304707:0.000000:0.000000
DF:@0.169570:0.340514:0.189140:0.340514:0.189140:0.324152:0.169570:0.324152:0.000000:0.000000
k:@0.269148:0.330030:0.276722:0.330030:0.276722:0.313669:0.269148:0.313669:0.000000
6:@0.220149:0.321068:0.229142:0.321068:0.229142:0.305398:0.220149:0.305398:0.000000
3:@0.220357:0.340520:0.229350:0.340520:0.229350:0.324850:0.220357:0.324850:0.000000
4:@0.249464:0.321072:0.258457:0.321072:0.258457:0.305402:0.249464:0.305402:0.000000
2:@0.249464:0.340520:0.258457:0.340520:0.258457:0.324850:0.249464:0.324850:0.000000
;:@0.261976:0.330023:0.265183:0.330023:0.265183:0.314353:0.261976:0.314353:0.000000
2:@0.294428:0.330023:0.303420:0.330023:0.303420:0.314353:0.294428:0.314353:0.000000
 :@0.095800:0.367585:0.099836:0.367585:0.099836:0.351915:0.095800:0.351915:0.000000
Conclusión::@0.124290:0.367585:0.213646:0.367585:0.213646:0.350960:0.124290:0.350960:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la razón de semejanza es 2, es decir, los lados correspondientes de :@0.213646:0.367585:0.698162:0.367585:0.698162:0.351915:0.213646:0.351915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
los dos triángulos son proporcionales y los ángulos   y  , ambos miden 60°. :@0.124290:0.384181:0.698256:0.384181:0.698256:0.368511:0.124290:0.368511:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.510884:0.384181:0.520779:0.384181:0.520779:0.367820:0.510884:0.367820:0.000000
D:@0.539244:0.384181:0.550779:0.384181:0.550779:0.367820:0.539244:0.367820:0.000000
Por lo tanto, se cumple el teorema LAL. Los dos triángulos son semejantes.:@0.124290:0.400777:0.667900:0.400777:0.667900:0.385108:0.124290:0.385108:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
b):@0.095801:0.448229:0.112460:0.448229:0.112460:0.431093:0.095801:0.431093:0.000000:0.000000
  En la figura, dado :@0.112459:0.448229:0.255126:0.448229:0.255126:0.432559:0.112459:0.432559:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
:@0.280622:0.449280:0.287993:0.449280:0.287993:0.432532:0.280622:0.432532:0.000000
AB DE:@0.259209:0.448409:0.309848:0.448409:0.309848:0.432048:0.259209:0.432048:0.000000:0.000000:0.000000:0.000000:0.000000
, demuestra: :@0.310763:0.448227:0.404394:0.448227:0.404394:0.432557:0.310763:0.432557:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ABC:@0.418787:0.448923:0.447074:0.448923:0.447074:0.433530:0.418787:0.433530:0.000000:0.000000:0.000000
EDC:@0.476374:0.448923:0.505858:0.448923:0.505858:0.433530:0.476374:0.433530:0.000000:0.000000:0.000000
.:@0.508037:0.448227:0.511244:0.448227:0.511244:0.432557:0.508037:0.432557:0.000000
 :@0.095793:0.634728:0.099829:0.634728:0.099829:0.619059:0.095793:0.619059:0.000000
Demostración:@0.270505:0.483664:0.375157:0.483664:0.375157:0.468086:0.270505:0.468086:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Enunciados:@0.149369:0.510909:0.235627:0.510909:0.235627:0.495331:0.149369:0.495331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Razones:@0.359393:0.510909:0.421662:0.510909:0.421662:0.495331:0.359393:0.495331:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
1. :@0.134291:0.539211:0.149050:0.539211:0.149050:0.524966:0.134291:0.524966:0.000000:0.000000:0.000000
:@0.174033:0.540710:0.181404:0.540710:0.181404:0.523961:0.174033:0.523961:0.000000
AB DE:@0.152620:0.539839:0.203259:0.539839:0.203259:0.523477:0.152620:0.523477:0.000000:0.000000:0.000000:0.000000:0.000000
2. :@0.134293:0.561848:0.149052:0.561848:0.149052:0.547602:0.134293:0.547602:0.000000:0.000000:0.000000
A:@0.163611:0.563006:0.173507:0.563006:0.173507:0.547612:0.163611:0.547612:0.000000
E:@0.203608:0.563006:0.211734:0.563006:0.211734:0.547612:0.203608:0.547612:0.000000
3. :@0.134293:0.584479:0.149052:0.584479:0.149052:0.570234:0.134293:0.570234:0.000000:0.000000:0.000000
1:@0.162774:0.586024:0.171767:0.586024:0.171767:0.570354:0.162774:0.570354:0.000000
2:@0.199629:0.586024:0.208622:0.586024:0.208622:0.570354:0.199629:0.570354:0.000000
4. :@0.134293:0.607110:0.149052:0.607110:0.149052:0.592865:0.134293:0.592865:0.000000:0.000000:0.000000
ABC:@0.161258:0.608713:0.189544:0.608713:0.189544:0.593320:0.161258:0.593320:0.000000:0.000000:0.000000
EDC:@0.218844:0.608713:0.248328:0.608713:0.248328:0.593320:0.218844:0.593320:0.000000:0.000000:0.000000
1.  Dado.:@0.269688:0.536381:0.326679:0.536381:0.326679:0.522136:0.269688:0.522136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2. Si dos rectas paralelas se cortan :@0.269688:0.551469:0.497433:0.551469:0.497433:0.537223:0.269688:0.537223:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por una transversal, los ángulos al-:@0.283927:0.566556:0.512629:0.566556:0.512629:0.552311:0.283927:0.552311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ternos internos son congruentes.:@0.283927:0.581644:0.503816:0.581644:0.503816:0.567399:0.283927:0.567399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3. Los ángulos opuestos por el vér-:@0.269688:0.596731:0.499782:0.596731:0.499782:0.582486:0.269688:0.582486:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
tice son congruentes.:@0.283927:0.611819:0.427142:0.611819:0.427142:0.597574:0.283927:0.597574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4. Criterio AAA.:@0.269688:0.626907:0.368693:0.626907:0.368693:0.612661:0.269688:0.612661:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Conclusión::@0.124290:0.658451:0.213646:0.658451:0.213646:0.641827:0.124290:0.641827:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 los triángulos :@0.213646:0.658451:0.320082:0.658451:0.320082:0.642781:0.213646:0.642781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
ABC:@0.334478:0.659637:0.362764:0.659637:0.362764:0.644244:0.334478:0.644244:0.000000:0.000000:0.000000
EDC:@0.392064:0.659637:0.421548:0.659637:0.421548:0.644244:0.392064:0.644244:0.000000:0.000000:0.000000
 son semejantes.:@0.427298:0.658451:0.548347:0.658451:0.548347:0.642781:0.427298:0.642781:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
c):@0.095803:0.705903:0.109900:0.705903:0.109900:0.688767:0.095803:0.688767:0.000000:0.000000
  Un triángulo tiene como medidas de sus lados 18  , 12   y 9  , y otro trián-:@0.109901:0.705903:0.694111:0.705903:0.694111:0.690233:0.109901:0.690233:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.495553:0.705903:0.510185:0.705903:0.510185:0.689542:0.495553:0.689542:0.000000
m:@0.540296:0.705903:0.554927:0.705903:0.554927:0.689542:0.540296:0.689542:0.000000
m:@0.585407:0.705903:0.600038:0.705903:0.600038:0.689542:0.585407:0.689542:0.000000
gulo tiene medidas 6  , 4   y 3  . ¿Cuál es la razón de semejanza? ¿Son seme-:@0.124292:0.722499:0.694130:0.722499:0.694130:0.706829:0.124292:0.706829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m:@0.280761:0.722499:0.295393:0.722499:0.295393:0.706138:0.280761:0.706138:0.000000
m:@0.314336:0.722499:0.328968:0.722499:0.328968:0.706138:0.314336:0.706138:0.000000
m:@0.356185:0.722499:0.370817:0.722499:0.370817:0.706138:0.356185:0.706138:0.000000
jantes estos triángulos?:@0.124292:0.739096:0.294783:0.739096:0.294783:0.723426:0.124292:0.723426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.095803:0.762815:0.099839:0.762815:0.099839:0.747145:0.095803:0.747145:0.000000
Aplicamos el teorema LLL: :@0.124292:0.762815:0.324692:0.762815:0.324692:0.747145:0.124292:0.747145:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.153975:0.788891:0.122151:0.788891:0.122151:0.773318:0.153975:0.773318:0.000000
=:@0.195917:0.788891:0.164092:0.788891:0.164092:0.773318:0.195917:0.773318:0.000000
AB:@0.130103:0.779255:0.148531:0.779255:0.148531:0.762894:0.130103:0.762894:0.000000:0.000000
DE:@0.128376:0.798704:0.148020:0.798704:0.148020:0.782343:0.128376:0.782343:0.000000:0.000000
AC:@0.170309:0.779255:0.189805:0.779255:0.189805:0.762894:0.170309:0.762894:0.000000:0.000000
DF:@0.169577:0.798704:0.189147:0.798704:0.189147:0.782343:0.169577:0.782343:0.000000:0.000000
BC:@0.210778:0.779255:0.229482:0.779255:0.229482:0.762894:0.210778:0.762894:0.000000:0.000000
EF:@0.212086:0.798704:0.228192:0.798704:0.228192:0.782343:0.212086:0.782343:0.000000:0.000000
 :@0.095800:0.816983:0.099836:0.816983:0.099836:0.801313:0.095800:0.801313:0.000000
Reemplazamos los valores con cada lado correspondiente: :@0.124290:0.816983:0.556818:0.816983:0.556818:0.801313:0.124290:0.801313:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.095800:0.863342:0.099836:0.863342:0.099836:0.847672:0.095800:0.847672:0.000000
=:@0.149735:0.850186:0.123992:0.850186:0.123992:0.834613:0.149735:0.834613:0.000000
=:@0.185596:0.850186:0.159852:0.850186:0.159852:0.834613:0.185596:0.834613:0.000000
=:@0.214177:0.850186:0.224294:0.850186:0.224294:0.834613:0.214177:0.834613:0.000000
18:@0.127217:0.840546:0.145000:0.840546:0.145000:0.824876:0.127217:0.824876:0.000000:0.000000
6:@0.132355:0.859999:0.141348:0.859999:0.141348:0.844329:0.132355:0.844329:0.000000
12:@0.163451:0.840550:0.181233:0.840550:0.181233:0.824880:0.163451:0.824880:0.000000:0.000000
4:@0.168424:0.859999:0.177417:0.859999:0.177417:0.844329:0.168424:0.844329:0.000000
9:@0.200463:0.840550:0.209456:0.840550:0.209456:0.824880:0.200463:0.824880:0.000000
3:@0.200830:0.859999:0.209823:0.859999:0.209823:0.844329:0.200830:0.844329:0.000000
3:@0.227582:0.849508:0.236575:0.849508:0.236575:0.833838:0.227582:0.833838:0.000000
Conclusión::@0.124295:0.887057:0.213651:0.887057:0.213651:0.870433:0.124295:0.870433:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 la razón de semejanza es 3. :@0.213651:0.887057:0.419727:0.887057:0.419727:0.871388:0.213651:0.871388:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.095806:0.910776:0.099841:0.910776:0.099841:0.895107:0.095806:0.895107:0.000000
Por lo tanto, los dos triángulos son semejantes.:@0.124295:0.910776:0.466473:0.910776:0.466473:0.895107:0.124295:0.895107:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Razón:@0.733044:0.321165:0.775880:0.321165:0.775880:0.306052:0.733044:0.306052:0.000000:0.000000:0.000000:0.000000:0.000000
Es el cociente entre :@0.733044:0.343381:0.866274:0.343381:0.866274:0.329136:0.733044:0.329136:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos números o :@0.733044:0.358469:0.836874:0.358469:0.836874:0.344224:0.733044:0.344224:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
dos cantidades :@0.733044:0.373557:0.837596:0.373557:0.837596:0.359311:0.733044:0.359311:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
comparables entre :@0.733044:0.388644:0.862220:0.388644:0.862220:0.374399:0.733044:0.374399:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
sí, y se expresa como :@0.733044:0.403732:0.876108:0.403732:0.876108:0.389487:0.733044:0.389487:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
fracción.:@0.733044:0.418820:0.789231:0.418820:0.789231:0.404574:0.733044:0.404574:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
a:@0.735734:0.443274:0.744161:0.443274:0.748521:0.428400:0.740094:0.428400:0.000000
b:@0.735731:0.461115:0.744158:0.461115:0.748518:0.446241:0.740091:0.446241:0.000000
antecedente:@0.777490:0.444648:0.860481:0.444648:0.860481:0.430403:0.777490:0.430403:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
consecuente:@0.776820:0.460993:0.861168:0.460993:0.861168:0.446748:0.776820:0.446748:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
→:@0.749396:0.443894:0.765930:0.443894:0.765930:0.429737:0.749396:0.429737:0.000000
→:@0.749078:0.461735:0.765612:0.461735:0.765612:0.447578:0.749078:0.447578:0.000000
Los términos de una :@0.733062:0.489660:0.872459:0.489660:0.872459:0.475414:0.733062:0.475414:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
razón se llaman: :@0.733062:0.504747:0.843427:0.504747:0.843427:0.490502:0.733062:0.490502:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
antecedente y :@0.733062:0.519835:0.832570:0.519835:0.832570:0.505590:0.733062:0.505590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
consecuente. :@0.733062:0.534922:0.825886:0.534922:0.825886:0.520677:0.733062:0.520677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El antecedente es :@0.733062:0.557139:0.854599:0.557139:0.854599:0.542894:0.733062:0.542894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el dividendo y el :@0.733062:0.572227:0.846392:0.572227:0.846392:0.557981:0.733062:0.557981:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
consecuente es el :@0.733062:0.587314:0.856526:0.587314:0.856526:0.573069:0.733062:0.573069:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
divisor.:@0.733062:0.602402:0.779014:0.602402:0.779014:0.588157:0.733062:0.588157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Proporción:@0.733062:0.624618:0.810174:0.624618:0.810174:0.609506:0.733062:0.609506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Proporción es una :@0.733062:0.646835:0.857432:0.646835:0.857432:0.632590:0.733062:0.632590:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
igualdad entre dos :@0.733062:0.661922:0.862004:0.661922:0.862004:0.647677:0.733062:0.647677:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
razones.:@0.733062:0.677010:0.787223:0.677010:0.787223:0.662765:0.733062:0.662765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.807835:0.710267:0.817952:0.710267:0.817952:0.694694:0.807835:0.694694:0.000000
a:@0.793756:0.700627:0.803025:0.700627:0.803025:0.684266:0.793756:0.684266:0.000000
b:@0.793542:0.720079:0.802811:0.720079:0.802811:0.703718:0.793542:0.703718:0.000000
c:@0.824063:0.700631:0.831729:0.700631:0.831729:0.684270:0.824063:0.684270:0.000000
d:@0.823068:0.720079:0.832337:0.720079:0.832337:0.703718:0.823068:0.703718:0.000000
Constante de :@0.733044:0.745320:0.829337:0.745320:0.829337:0.730208:0.733044:0.730208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
proporcionalidad o :@0.733044:0.760408:0.870263:0.760408:0.870263:0.745295:0.733044:0.745295:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
razón de semejanza:@0.733044:0.775496:0.871084:0.775496:0.871084:0.760383:0.733044:0.760383:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Es el cociente entre :@0.733044:0.797712:0.866274:0.797712:0.866274:0.783467:0.733044:0.783467:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el antecedente y :@0.733044:0.812800:0.847897:0.812800:0.847897:0.798555:0.733044:0.798555:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el consecuente de :@0.733044:0.827887:0.859372:0.827887:0.859372:0.813642:0.733044:0.813642:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
cualquier razón de una :@0.733044:0.842975:0.889560:0.842975:0.889560:0.828730:0.733044:0.828730:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
proporción.:@0.733044:0.858063:0.810658:0.858063:0.810658:0.843817:0.733044:0.843817:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.781031:0.891328:0.761037:0.891328:0.761037:0.875755:0.781031:0.875755:0.000000
=:@0.811142:0.891328:0.791148:0.891328:0.791148:0.875755:0.811142:0.875755:0.000000
=:@0.839299:0.891328:0.849416:0.891328:0.849416:0.875755:0.839299:0.875755:0.000000
a:@0.766952:0.881689:0.776221:0.881689:0.776221:0.865327:0.766952:0.865327:0.000000
b:@0.766738:0.901140:0.776007:0.901140:0.776007:0.884779:0.766738:0.884779:0.000000
c:@0.797259:0.881692:0.804925:0.881692:0.804925:0.865331:0.797259:0.865331:0.000000
d:@0.796264:0.901140:0.805533:0.901140:0.805533:0.884779:0.796264:0.884779:0.000000
e:@0.826366:0.881692:0.834161:0.881692:0.834161:0.865331:0.826366:0.865331:0.000000
f:@0.826524:0.901140:0.831223:0.901140:0.831223:0.884779:0.826524:0.884779:0.000000
k:@0.852700:0.890651:0.860273:0.890651:0.860273:0.874289:0.852700:0.874289:0.000000
¿Sabías que?:@0.765616:0.296654:0.867484:0.296654:0.867484:0.279753:0.765616:0.279753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.575416:0.472758:0.582171:0.472758:0.582171:0.462019:0.575416:0.462019:0.000000
B:@0.684509:0.472758:0.690682:0.472758:0.690682:0.462019:0.684509:0.462019:0.000000
C:@0.586275:0.534424:0.592876:0.534424:0.592876:0.523685:0.586275:0.523685:0.000000
D:@0.531372:0.569239:0.539067:0.569239:0.539067:0.558500:0.531372:0.558500:0.000000
E:@0.580531:0.569239:0.586121:0.569239:0.586121:0.558500:0.580531:0.558500:0.000000
2:@0.575404:0.540968:0.581506:0.540968:0.581506:0.530238:0.575404:0.530238:0.000000
1:@0.584860:0.522168:0.590961:0.522168:0.590961:0.511438:0.584860:0.511438:0.000000
A:@0.505463:0.875722:0.514930:0.875722:0.514930:0.860673:0.505463:0.860673:0.000000
E:@0.548931:0.804419:0.556765:0.804419:0.556765:0.789370:0.548931:0.789370:0.000000
18:@0.529480:0.841534:0.546581:0.841534:0.546581:0.826498:0.529480:0.826498:0.000000:0.000000
 m:@0.546581:0.841534:0.563082:0.841534:0.563082:0.826485:0.546581:0.826485:0.000000:0.000000
12:@0.582816:0.879900:0.599917:0.879900:0.599917:0.864864:0.582816:0.864864:0.000000:0.000000
 m:@0.599917:0.879900:0.616418:0.879900:0.616418:0.864851:0.599917:0.864851:0.000000:0.000000
9 :@0.668370:0.841534:0.680454:0.841534:0.680454:0.826498:0.668370:0.826498:0.000000:0.000000
m:@0.680454:0.841534:0.693921:0.841534:0.693921:0.826485:0.680454:0.826485:0.000000
3 :@0.559482:0.778150:0.571566:0.778150:0.571566:0.763113:0.559482:0.763113:0.000000:0.000000
m:@0.571566:0.778150:0.585033:0.778150:0.585033:0.763101:0.571566:0.763101:0.000000
6 :@0.477261:0.783153:0.489345:0.783153:0.489345:0.768117:0.477261:0.768117:0.000000:0.000000
m:@0.489345:0.783153:0.502812:0.783153:0.502812:0.768105:0.489345:0.768105:0.000000
4 :@0.492712:0.748966:0.504796:0.748966:0.504796:0.733929:0.492712:0.733929:0.000000:0.000000
m:@0.504796:0.748966:0.518263:0.748966:0.518263:0.733917:0.504796:0.733917:0.000000
D:@0.428092:0.757722:0.438876:0.757722:0.438876:0.742673:0.428092:0.742673:0.000000
F:@0.547315:0.748966:0.555065:0.748966:0.555065:0.733917:0.547315:0.733917:0.000000
B:@0.659903:0.791910:0.668554:0.791910:0.668554:0.776861:0.659903:0.776861:0.000000
C:@0.659903:0.881977:0.669154:0.881977:0.669154:0.866928:0.659903:0.866928:0.000000
A:@0.720337:0.237217:0.727534:0.237217:0.727534:0.225318:0.720337:0.225318:0.000000
D:@0.828799:0.237388:0.837188:0.237388:0.837188:0.225489:0.828799:0.225489:0.000000
C:@0.808843:0.237217:0.816054:0.237217:0.816054:0.225318:0.808843:0.225318:0.000000
F:@0.904841:0.237388:0.910698:0.237388:0.910698:0.225489:0.904841:0.225489:0.000000
3:@0.843193:0.217030:0.849733:0.217030:0.849733:0.205634:0.843193:0.205634:0.000000
6:@0.738510:0.204156:0.745050:0.204156:0.745050:0.192759:0.738510:0.192759:0.000000
1:@0.764749:0.216558:0.772831:0.216558:0.772831:0.202730:0.764749:0.202730:0.000000
2:@0.868360:0.224852:0.876441:0.224852:0.876441:0.211024:0.868360:0.211024:0.000000
60:@0.736465:0.229635:0.747092:0.229635:0.747092:0.220375:0.736465:0.220375:0.000000:0.000000
60:@0.846237:0.229839:0.856865:0.229839:0.856865:0.220580:0.846237:0.220580:0.000000:0.000000
B:@0.763964:0.170941:0.770397:0.170941:0.770397:0.159042:0.763964:0.159042:0.000000
E:@0.869450:0.192124:0.875360:0.192124:0.875360:0.180225:0.869450:0.180225:0.000000
4:@0.765309:0.242393:0.771849:0.242393:0.771849:0.230996:0.765309:0.230996:0.000000
2:@0.868102:0.242393:0.874642:0.242393:0.874642:0.230996:0.868102:0.230996:0.000000
 ©:@0.079553:0.731952:0.079553:0.720342:0.061505:0.720342:0.061505:0.731952:0.000000:0.000000
maya:@0.080774:0.720340:0.080774:0.684191:0.055786:0.684191:0.055786:0.720340:0.000000:0.000000:0.000000:0.000000
®EDUCACIÓN – Libro resuelto solo para fines didácticos – Prohibida su reproducción :@0.079553:0.684191:0.079553:0.268044:0.061505:0.268044:0.061505:0.684191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000