194:@0.067867:0.963104:0.109245:0.963104:0.109245:0.941283:0.067867:0.941283:0.000000:0.000000:0.000000 Matemática:@0.120102:0.956142:0.204868:0.956142:0.204868:0.943479:0.120102:0.943479:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 10.º EGB:@0.120102:0.967458:0.179272:0.967458:0.179272:0.954794:0.120102:0.954794:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Evaluación sumativa:@0.077364:0.090296:0.368210:0.090296:0.368210:0.064164:0.077364:0.064164:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 DUA:@0.769036:0.079446:0.812680:0.079446:0.812680:0.059195:0.769036:0.059195:0.000000:0.000000:0.000000 Acción y expresión:@0.716439:0.093905:0.865277:0.093905:0.865277:0.077005:0.716439:0.077005:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1. Escribe:@0.072616:0.152346:0.158175:0.152346:0.158175:0.135445:0.072616:0.135445:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.086842:0.152346:0.090877:0.152346:0.090877:0.135957:0.086842:0.135957:0.000000 (V) si la afirmación es verdadera o (F) si la :@0.158175:0.152346:0.477839:0.152346:0.477839:0.135957:0.158175:0.135957:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 afirmación es falsa.:@0.101105:0.168942:0.238593:0.168942:0.238593:0.152553:0.101105:0.152553:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a) :@0.101105:0.196229:0.119827:0.196229:0.119827:0.179329:0.101105:0.179329:0.000000:0.000000:0.000000 Dos triángulos pueden ser congruentes si :@0.129594:0.196229:0.477913:0.196229:0.477913:0.179841:0.129594:0.179841:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tienen todos sus lados son iguales.:@0.129594:0.212826:0.382841:0.212826:0.382841:0.196437:0.129594:0.196437:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 (:@0.424267:0.212826:0.429150:0.212826:0.429150:0.196437:0.424267:0.196437:0.000000 ____:@0.433188:0.212513:0.464079:0.212513:0.464079:0.197614:0.433188:0.197614:0.000000:0.000000:0.000000:0.000000 ):@0.462404:0.212827:0.471323:0.212827:0.471323:0.196438:0.462404:0.196438:0.000000:0.000000 b) :@0.101112:0.240114:0.121142:0.240114:0.121142:0.223214:0.101112:0.223214:0.000000:0.000000:0.000000 Dos triángulos pueden ser congruentes si :@0.129601:0.240114:0.477920:0.240114:0.477920:0.223725:0.129601:0.223725:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tienen todos sus ángulos iguales. :@0.129601:0.256711:0.375954:0.256711:0.375954:0.240322:0.129601:0.240322:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( :@0.424277:0.256711:0.433196:0.256711:0.433196:0.240322:0.424277:0.240322:0.000000:0.000000 ____:@0.433188:0.256398:0.464079:0.256398:0.464079:0.241499:0.433188:0.241499:0.000000:0.000000:0.000000:0.000000 ):@0.462404:0.256712:0.471323:0.256712:0.471323:0.240323:0.462404:0.240323:0.000000:0.000000 c) :@0.101112:0.283999:0.118378:0.283999:0.118378:0.267099:0.101112:0.267099:0.000000:0.000000:0.000000 Es lo mismo congruencia y semejanza. ( :@0.129601:0.283999:0.433196:0.283999:0.433196:0.267610:0.129601:0.267610:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ____:@0.433188:0.283686:0.464079:0.283686:0.464079:0.268787:0.433188:0.268787:0.000000:0.000000:0.000000:0.000000 ):@0.462404:0.284000:0.471323:0.284000:0.471323:0.267611:0.462404:0.267611:0.000000:0.000000 d):@0.101112:0.311288:0.117365:0.311288:0.117365:0.294387:0.101112:0.294387:0.000000:0.000000 Un postulado de congruencia es L.A.L. :@0.117365:0.311288:0.393134:0.311288:0.393134:0.294899:0.117365:0.294899:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ( :@0.424277:0.311288:0.433196:0.311288:0.433196:0.294899:0.424277:0.294899:0.000000:0.000000 ____:@0.433188:0.310975:0.464079:0.310975:0.464079:0.296076:0.433188:0.296076:0.000000:0.000000:0.000000:0.000000 ):@0.462404:0.311289:0.471323:0.311289:0.471323:0.294900:0.462404:0.294900:0.000000:0.000000 2. Encuentra:@0.072622:0.355172:0.183557:0.355172:0.183557:0.338272:0.072622:0.338272:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la medida del ángulo si en el triángu-:@0.183741:0.355172:0.473884:0.355172:0.473884:0.338784:0.183741:0.338784:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 x:@0.348503:0.355172:0.355966:0.355172:0.355966:0.339779:0.348503:0.339779:0.000000 lo ABC: :@0.101112:0.374120:0.160725:0.374120:0.160725:0.357731:0.101112:0.357731:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AD CD DB:@0.162690:0.374285:0.263563:0.374285:0.268367:0.357896:0.167494:0.357896:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ≅:@0.191293:0.374962:0.161938:0.374962:0.161938:0.359389:0.191293:0.359389:0.000000 ≅:@0.230765:0.374962:0.201410:0.374962:0.201410:0.359389:0.230765:0.359389:0.000000 A:@0.199735:0.521167:0.209776:0.521167:0.209776:0.506366:0.199735:0.506366:0.000000 D:@0.290628:0.449785:0.301555:0.449785:0.301555:0.434984:0.290628:0.434984:0.000000 40º:@0.238438:0.513077:0.261096:0.513077:0.261096:0.498276:0.238438:0.498276:0.000000:0.000000:0.000000 x:@0.347297:0.496786:0.353942:0.496786:0.353942:0.483081:0.347297:0.483081:0.000000 B:@0.365804:0.396442:0.374697:0.396442:0.374697:0.381641:0.365804:0.381641:0.000000 C:@0.365493:0.525341:0.375008:0.525341:0.375008:0.510540:0.365493:0.510540:0.000000 3. Aplica:@0.072616:0.636519:0.150601:0.636519:0.150601:0.619618:0.072616:0.619618:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.086842:0.636519:0.090877:0.636519:0.090877:0.620130:0.086842:0.620130:0.000000 la semejanza de triángulos en cada gráfico y :@0.150601:0.636519:0.477966:0.636519:0.477966:0.620130:0.150601:0.620130:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 demuestra:@0.101105:0.653115:0.186847:0.653115:0.186847:0.636214:0.101105:0.636214:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 las siguientes igualdades.:@0.186847:0.653115:0.375855:0.653115:0.375855:0.636726:0.186847:0.636726:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 a) :@0.101105:0.680402:0.119827:0.680402:0.119827:0.663502:0.101105:0.663502:0.000000:0.000000:0.000000 :@0.129594:0.680402:0.133630:0.680402:0.133630:0.664013:0.129594:0.664013:0.000000 AB:@0.133636:0.680404:0.152377:0.680404:0.152377:0.665010:0.133636:0.665010:0.000000:0.000000 ×:@0.152635:0.680404:0.167654:0.680404:0.167654:0.664015:0.152635:0.664015:0.000000:0.000000 :@0.167654:0.679989:0.172261:0.679989:0.172261:0.663046:0.167654:0.663046:0.000000 EC:@0.172256:0.680404:0.190296:0.680404:0.190296:0.665010:0.172256:0.665010:0.000000:0.000000 = :@0.195990:0.679989:0.210714:0.679989:0.210714:0.663046:0.195990:0.663046:0.000000:0.000000 ED:@0.210719:0.680404:0.230381:0.680404:0.230381:0.665010:0.210719:0.665010:0.000000:0.000000 ×:@0.232095:0.680404:0.247114:0.680404:0.247114:0.664015:0.232095:0.664015:0.000000:0.000000 :@0.247114:0.679989:0.251721:0.679989:0.251721:0.663046:0.247114:0.663046:0.000000 BC:@0.251714:0.680404:0.270473:0.680404:0.270473:0.665010:0.251714:0.665010:0.000000:0.000000 B:@0.204293:0.705381:0.214370:0.705381:0.214370:0.687634:0.204293:0.687634:0.000000 D:@0.277626:0.747689:0.290536:0.747689:0.290536:0.729942:0.277626:0.729942:0.000000 C:@0.341659:0.789772:0.353033:0.789772:0.353033:0.772025:0.341659:0.772025:0.000000 E:@0.221035:0.800465:0.230334:0.800465:0.230334:0.782718:0.221035:0.782718:0.000000 A:@0.193318:0.789772:0.204991:0.789772:0.204991:0.772025:0.193318:0.772025:0.000000 F:@0.196531:0.747689:0.205750:0.747689:0.205750:0.729942:0.196531:0.729942:0.000000 b) :@0.530866:0.152346:0.550897:0.152346:0.550897:0.135445:0.530866:0.135445:0.000000:0.000000:0.000000 :@0.559355:0.152346:0.563391:0.152346:0.563391:0.135957:0.559355:0.135957:0.000000 BC:@0.563394:0.152346:0.582153:0.152346:0.582153:0.136953:0.563394:0.136953:0.000000:0.000000 ×:@0.582393:0.152346:0.597411:0.152346:0.597411:0.135957:0.582393:0.135957:0.000000:0.000000 :@0.597411:0.151931:0.602018:0.151931:0.602018:0.134989:0.597411:0.134989:0.000000 AD AB:@0.602013:0.152346:0.663826:0.152346:0.663826:0.136953:0.602013:0.136953:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 = :@0.625748:0.151931:0.645079:0.151931:0.645079:0.134989:0.625748:0.134989:0.000000:0.000000:0.000000 ×:@0.666461:0.152346:0.681480:0.152346:0.681480:0.135957:0.666461:0.135957:0.000000:0.000000 :@0.681480:0.151931:0.686087:0.151931:0.686087:0.134989:0.681480:0.134989:0.000000 AH:@0.686079:0.152346:0.707086:0.152346:0.707086:0.136953:0.686079:0.136953:0.000000:0.000000 B:@0.590744:0.260901:0.599204:0.260901:0.599204:0.246002:0.590744:0.246002:0.000000 D:@0.724596:0.207177:0.735434:0.207177:0.735434:0.192278:0.724596:0.192278:0.000000 C:@0.806280:0.260901:0.815829:0.260901:0.815829:0.246002:0.806280:0.246002:0.000000 H:@0.664622:0.268659:0.675176:0.268659:0.675176:0.253760:0.664622:0.253760:0.000000 A:@0.664991:0.174927:0.674791:0.174927:0.674791:0.160028:0.664991:0.160028:0.000000 4. Halla:@0.502373:0.379027:0.571440:0.379027:0.571440:0.362127:0.502373:0.362127:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.516600:0.379027:0.520635:0.379027:0.520635:0.362638:0.516600:0.362638:0.000000 la suma de los ángulos señalados.:@0.571440:0.379027:0.822253:0.379027:0.822253:0.362638:0.571440:0.362638:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 β:@0.837862:0.406641:0.846347:0.406641:0.846347:0.392973:0.837862:0.392973:0.000000 α:@0.572955:0.483978:0.581304:0.483978:0.581304:0.470310:0.572955:0.470310:0.000000 5.:@0.502373:0.603857:0.516600:0.603857:0.516600:0.586956:0.502373:0.586956:0.000000:0.000000 En la figura puedes observar una torre y un :@0.516600:0.603857:0.907651:0.603857:0.907651:0.587468:0.516600:0.587468:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 poste cuyas sombras, en un momento dado, se :@0.530863:0.620453:0.907632:0.620453:0.907632:0.604064:0.530863:0.604064:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 superponen. A partir de los datos de la figura, :@0.530863:0.637049:0.907722:0.637049:0.907722:0.620660:0.530863:0.620660:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 determina:@0.530863:0.653646:0.613750:0.653646:0.613750:0.636745:0.530863:0.636745:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 la altura de la torre.:@0.613750:0.653646:0.757134:0.653646:0.757134:0.637257:0.613750:0.637257:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5 m:@0.738272:0.748894:0.762328:0.748894:0.762328:0.734874:0.738272:0.734874:0.000000:0.000000:0.000000 1,8 km:@0.742103:0.819480:0.783608:0.819480:0.783608:0.805460:0.742103:0.805460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2,2 km:@0.636672:0.819480:0.678178:0.819480:0.678178:0.805460:0.636672:0.805460:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Poste:@0.666577:0.745345:0.700769:0.745345:0.700769:0.731325:0.666577:0.731325:0.000000:0.000000:0.000000:0.000000:0.000000 Torre:@0.583042:0.671920:0.614602:0.671920:0.614602:0.657900:0.583042:0.657900:0.000000:0.000000:0.000000:0.000000:0.000000