161:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000 Pensamiento espacial, métrico, numérico y variacional:@0.444620:0.043661:0.926912:0.043661:0.926912:0.024916:0.444620:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Trabajo colaborativo:@0.089309:0.139215:0.244769:0.139215:0.244769:0.122546:0.089309:0.122546:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 2. Describa la trayectoria que toma una pelota de fútbol debido a un saque de arquero.:@0.089691:0.165426:0.758646:0.165426:0.758646:0.148757:0.089691:0.148757:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3. Analicen la siguiente demostración y respondan.:@0.089691:0.234448:0.487845:0.234448:0.487845:0.217779:0.089691:0.217779:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Las diagonales de un paralelogramo se bisectan.:@0.119816:0.265388:0.471067:0.265388:0.471067:0.248954:0.119816:0.248954:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Considérese el paralelogramo que tiene como vértices los puntos :@0.119816:0.296328:0.616716:0.296328:0.616716:0.279894:0.119816:0.279894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.341311:0.296328:0.350073:0.296328:0.350073:0.279922:0.341311:0.279922:0.000000 A, B, C, D,:@0.617033:0.296328:0.680157:0.296328:0.680157:0.279922:0.617033:0.279922:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 tal que los segmentos de recta :@0.680096:0.296328:0.913590:0.296328:0.913590:0.279894:0.680096:0.279894:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 3:@0.119816:0.313552:0.123903:0.313552:0.123903:0.295898:0.119816:0.295898:0.000000 A B B C C D A D:@0.123811:0.312970:0.274327:0.312970:0.274327:0.296564:0.123811:0.296564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , , , , , , , son los lados de y satisfacen las condiciones de paralelismo siguientes: :@0.133622:0.312970:0.803454:0.312970:0.803454:0.296536:0.133622:0.296536:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4 3:@0.149065:0.313552:0.163828:0.313552:0.163828:0.295898:0.149065:0.295898:0.000000:0.000000:0.000000 4 3:@0.189009:0.313552:0.203772:0.313552:0.203772:0.295898:0.189009:0.295898:0.000000:0.000000:0.000000 4 3:@0.231640:0.313552:0.246403:0.313552:0.246403:0.295898:0.231640:0.295898:0.000000:0.000000:0.000000 4:@0.274253:0.313552:0.278340:0.313552:0.278340:0.295898:0.274253:0.295898:0.000000 P:@0.399938:0.312970:0.408700:0.312970:0.408700:0.296564:0.399938:0.296564:0.000000 3:@0.802670:0.313552:0.806757:0.313552:0.806757:0.295898:0.802670:0.295898:0.000000 A, B:@0.806665:0.312970:0.831496:0.312970:0.831496:0.296564:0.806665:0.296564:0.000000:0.000000:0.000000:0.000000 4 3:@0.831441:0.313552:0.854284:0.313552:0.854284:0.295898:0.831441:0.295898:0.000000:0.000000:0.000000 || :@0.835435:0.312970:0.850676:0.312970:0.850676:0.296536:0.835435:0.296536:0.000000:0.000000:0.000000:0.000000 C, D A, :@0.854192:0.312970:0.912801:0.312970:0.912801:0.296564:0.854192:0.296564:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 4 3:@0.881674:0.313552:0.896437:0.313552:0.896437:0.295898:0.881674:0.295898:0.000000:0.000000:0.000000 , :@0.885669:0.312970:0.892829:0.312970:0.892829:0.296536:0.885669:0.296536:0.000000:0.000000 D:@0.119780:0.329612:0.131302:0.329612:0.131302:0.313206:0.119780:0.313206:0.000000 4 3:@0.131339:0.330194:0.156741:0.330194:0.156741:0.312540:0.131339:0.312540:0.000000:0.000000:0.000000 || :@0.135462:0.329612:0.152029:0.329612:0.152029:0.313178:0.135462:0.313178:0.000000:0.000000:0.000000:0.000000 B, C:@0.156797:0.329612:0.182488:0.329612:0.182488:0.313206:0.156797:0.313206:0.000000:0.000000:0.000000:0.000000 4:@0.182511:0.330194:0.186598:0.330194:0.186598:0.312540:0.182511:0.312540:0.000000 . En la Figura 3.10. se muestra el paralelogramo con sus vértices y el punto O intersección de las :@0.186635:0.329612:0.913465:0.329612:0.913465:0.313178:0.186635:0.313178:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.538802:0.329612:0.547564:0.329612:0.547564:0.313206:0.538802:0.313206:0.000000 diagonales. En la Figura 3.11. se muestra el paralelogramo y los vectores :@0.119780:0.346254:0.654039:0.346254:0.654039:0.329820:0.119780:0.329820:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 P:@0.539778:0.346254:0.548540:0.346254:0.548540:0.329847:0.539778:0.329847:0.000000 AB BC AD DC:@0.653884:0.346254:0.763776:0.346254:0.763776:0.329847:0.653884:0.329847:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 , :@0.672476:0.346254:0.679636:0.346254:0.679636:0.329820:0.672476:0.329820:0.000000:0.000000 , :@0.698154:0.346254:0.705314:0.346254:0.705314:0.329820:0.698154:0.329820:0.000000:0.000000 y :@0.726501:0.346254:0.742515:0.346254:0.742515:0.329820:0.726501:0.329820:0.000000:0.000000:0.000000 .:@0.763720:0.346254:0.766923:0.346254:0.766923:0.329820:0.763720:0.329820:0.000000 A:@0.249518:0.470766:0.259403:0.470766:0.259403:0.454360:0.249518:0.454360:0.000000 D:@0.274110:0.388320:0.285633:0.388320:0.285633:0.371913:0.274110:0.371913:0.000000 B:@0.451942:0.470766:0.460778:0.470766:0.460778:0.454360:0.451942:0.454360:0.000000 P:@0.251175:0.426721:0.259936:0.426721:0.259936:0.410315:0.251175:0.410315:0.000000 O:@0.361057:0.407556:0.362137:0.407556:0.362137:0.406065:0.361057:0.406065:0.000000 C:@0.467654:0.388317:0.477557:0.388317:0.477557:0.371911:0.467654:0.371911:0.000000 A:@0.510245:0.470766:0.520130:0.470766:0.520130:0.454360:0.510245:0.454360:0.000000 D:@0.534256:0.388317:0.545779:0.388317:0.545779:0.371911:0.534256:0.371911:0.000000 B:@0.716709:0.470763:0.725544:0.470763:0.725544:0.454357:0.716709:0.454357:0.000000 G:@0.623035:0.420158:0.633932:0.420158:0.633932:0.403752:0.623035:0.403752:0.000000 C:@0.733386:0.386819:0.743289:0.386819:0.743289:0.370413:0.733386:0.370413:0.000000 Figura 3.11:@0.593031:0.506016:0.671843:0.506016:0.671843:0.489583:0.593031:0.489583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Figura 3.10:@0.327414:0.506016:0.406227:0.506016:0.406227:0.489583:0.327414:0.489583:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 Se tiene :@0.119799:0.543890:0.182081:0.543890:0.182081:0.527457:0.119799:0.527457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AD:@0.181960:0.543890:0.203294:0.543890:0.203294:0.527484:0.181960:0.527484:0.000000:0.000000 :@0.203239:0.543890:0.226469:0.543890:0.226469:0.527457:0.203239:0.527457:0.000000:0.000000:0.000000 5:@0.207196:0.543336:0.222529:0.543336:0.222529:0.529620:0.207196:0.529620:0.000000 BC AB:@0.226395:0.543890:0.279574:0.543890:0.279574:0.527484:0.226395:0.527484:0.000000:0.000000:0.000000:0.000000:0.000000 y :@0.245005:0.543890:0.261019:0.543890:0.261019:0.527457:0.245005:0.527457:0.000000:0.000000:0.000000 :@0.279518:0.543890:0.302748:0.543890:0.302748:0.527457:0.279518:0.527457:0.000000:0.000000:0.000000 5:@0.283476:0.543336:0.298809:0.543336:0.298809:0.529620:0.283476:0.529620:0.000000 DC:@0.302675:0.543890:0.324027:0.543890:0.324027:0.527484:0.302675:0.527484:0.000000:0.000000 . Además de la adición de vectores, tenemos: :@0.323972:0.543890:0.694676:0.543890:0.694676:0.527457:0.323972:0.527457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AB:@0.652854:0.543890:0.671501:0.543890:0.671501:0.527484:0.652854:0.527484:0.000000:0.000000 1:@0.675403:0.543336:0.690736:0.543336:0.690736:0.529620:0.675403:0.529620:0.000000 BC:@0.694602:0.543890:0.713267:0.543890:0.713267:0.527484:0.694602:0.527484:0.000000:0.000000 :@0.713212:0.543890:0.736442:0.543890:0.736442:0.527457:0.713212:0.527457:0.000000:0.000000:0.000000 5:@0.717169:0.543336:0.732502:0.543336:0.732502:0.529620:0.717169:0.529620:0.000000 AC:@0.736368:0.543890:0.755769:0.543890:0.755769:0.527484:0.736368:0.527484:0.000000:0.000000 .:@0.755714:0.543890:0.758917:0.543890:0.758917:0.527457:0.755714:0.527457:0.000000 Puesto que es el punto medio del segmento , entonces: :@0.119891:0.579393:0.562504:0.579393:0.562504:0.562959:0.119891:0.562959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 O:@0.205595:0.579393:0.217467:0.579393:0.217467:0.562987:0.205595:0.562987:0.000000 AB:@0.462229:0.579393:0.480875:0.579393:0.480875:0.562987:0.462229:0.562987:0.000000:0.000000 AO:@0.562346:0.579393:0.583717:0.579393:0.583717:0.562987:0.562346:0.562987:0.000000:0.000000 :@0.583661:0.579393:0.630958:0.579396:0.630958:0.562962:0.583661:0.562959:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.587619:0.578838:0.602952:0.578838:0.602952:0.565123:0.587619:0.565123:0.000000 1:@0.610397:0.573155:0.619380:0.573155:0.619380:0.556721:0.610397:0.556721:0.000000 2:@0.610397:0.587134:0.619380:0.587134:0.619380:0.570700:0.610397:0.570700:0.000000 AC:@0.630866:0.579396:0.650267:0.579396:0.650267:0.562989:0.630866:0.562989:0.000000:0.000000 (:@0.650212:0.579396:0.698436:0.579396:0.698436:0.562962:0.650212:0.562962:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.654170:0.578841:0.669503:0.578841:0.669503:0.565125:0.654170:0.565125:0.000000 1:@0.677028:0.573155:0.686011:0.573155:0.686011:0.556721:0.677028:0.556721:0.000000 2:@0.677028:0.587134:0.686011:0.587134:0.686011:0.570700:0.677028:0.570700:0.000000 AB:@0.698344:0.579396:0.716990:0.579396:0.716990:0.562989:0.698344:0.562989:0.000000:0.000000 :@0.716935:0.579396:0.720966:0.579396:0.720966:0.562962:0.716935:0.562962:0.000000 1 :@0.720892:0.578841:0.740736:0.578841:0.740736:0.565125:0.720892:0.565125:0.000000:0.000000 BC:@0.740643:0.579396:0.759308:0.579396:0.759308:0.562989:0.740643:0.562989:0.000000:0.000000 ).:@0.759253:0.579396:0.767260:0.579396:0.767260:0.562962:0.759253:0.562962:0.000000:0.000000 Por otro lado, :@0.119822:0.610335:0.220285:0.610335:0.220285:0.593902:0.119822:0.593902:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AB:@0.220123:0.610335:0.238770:0.610335:0.238770:0.593929:0.220123:0.593929:0.000000:0.000000 :@0.238714:0.610335:0.261944:0.610335:0.261944:0.593902:0.238714:0.593902:0.000000:0.000000:0.000000 1:@0.242672:0.609781:0.258005:0.609781:0.258005:0.596065:0.242672:0.596065:0.000000 BC:@0.261871:0.610335:0.280536:0.610335:0.280536:0.593929:0.261871:0.593929:0.000000:0.000000 :@0.280481:0.610335:0.303710:0.610335:0.303710:0.593902:0.280481:0.593902:0.000000:0.000000:0.000000 5:@0.284438:0.609781:0.299771:0.609781:0.299771:0.596065:0.284438:0.596065:0.000000 AC:@0.303637:0.610335:0.323038:0.610335:0.323038:0.593929:0.303637:0.593929:0.000000:0.000000 :@0.322983:0.610335:0.327014:0.610335:0.327014:0.593902:0.322983:0.593902:0.000000 ⇒ :@0.326940:0.609919:0.349618:0.609919:0.349618:0.592931:0.326940:0.592931:0.000000:0.000000 BD:@0.349526:0.610335:0.369811:0.610335:0.369811:0.593929:0.349526:0.593929:0.000000:0.000000 :@0.369756:0.610335:0.392986:0.610335:0.392986:0.593902:0.369756:0.593902:0.000000:0.000000:0.000000 5:@0.373713:0.609781:0.389047:0.609781:0.389047:0.596065:0.373713:0.596065:0.000000 AD:@0.392912:0.610335:0.414246:0.610335:0.414246:0.593929:0.392912:0.593929:0.000000:0.000000 :@0.414191:0.610335:0.437421:0.610335:0.437421:0.593902:0.414191:0.593902:0.000000:0.000000:0.000000 2:@0.418148:0.609781:0.433482:0.609781:0.433482:0.596065:0.418148:0.596065:0.000000 AB:@0.437347:0.610335:0.455994:0.610335:0.455994:0.593929:0.437347:0.593929:0.000000:0.000000 .:@0.455938:0.610335:0.459141:0.610335:0.459141:0.593902:0.455938:0.593902:0.000000 Denotamos con con al punto medio del segmento , . Entonces,:@0.119896:0.641275:0.620595:0.641275:0.620595:0.624842:0.119896:0.624842:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 G:@0.272657:0.641275:0.283555:0.641275:0.283555:0.624869:0.272657:0.624869:0.000000 3:@0.508160:0.641858:0.512246:0.641858:0.512246:0.624204:0.508160:0.624204:0.000000 B D:@0.512154:0.641275:0.539507:0.641275:0.539507:0.624869:0.512154:0.624869:0.000000:0.000000:0.000000 4:@0.539434:0.641858:0.543520:0.641858:0.543520:0.624204:0.539434:0.624204:0.000000 BG:@0.119859:0.676778:0.139518:0.676778:0.139518:0.660372:0.119859:0.660372:0.000000:0.000000 :@0.139463:0.676778:0.186786:0.676768:0.186786:0.660334:0.139463:0.660344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.143420:0.676223:0.158753:0.676223:0.158753:0.662508:0.143420:0.662508:0.000000 1:@0.166225:0.670527:0.175208:0.670527:0.175208:0.654093:0.166225:0.654093:0.000000 2:@0.166225:0.684506:0.175208:0.684506:0.175208:0.668073:0.166225:0.668073:0.000000 BD:@0.186694:0.676768:0.206979:0.676768:0.206979:0.660362:0.186694:0.660362:0.000000:0.000000 (:@0.206923:0.676768:0.255145:0.676768:0.255145:0.660334:0.206923:0.660334:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.210881:0.676213:0.226214:0.676213:0.226214:0.662498:0.210881:0.662498:0.000000 1:@0.233738:0.670527:0.242721:0.670527:0.242721:0.654093:0.233738:0.654093:0.000000 2:@0.233738:0.684506:0.242721:0.684506:0.242721:0.668073:0.233738:0.668073:0.000000 AD:@0.255053:0.676768:0.276387:0.676768:0.276387:0.660362:0.255053:0.660362:0.000000:0.000000 :@0.276332:0.676768:0.280363:0.676768:0.280363:0.660334:0.276332:0.660334:0.000000 2 :@0.280290:0.676213:0.300133:0.676213:0.300133:0.662498:0.280290:0.662498:0.000000:0.000000 AB:@0.300041:0.676768:0.318687:0.676768:0.318687:0.660362:0.300041:0.660362:0.000000:0.000000 ) :@0.318632:0.676768:0.327468:0.676768:0.327468:0.660334:0.318632:0.660334:0.000000:0.000000 5 :@0.327376:0.676213:0.347219:0.676213:0.347219:0.662498:0.327376:0.662498:0.000000:0.000000 1:@0.350793:0.670527:0.359776:0.670527:0.359776:0.654093:0.350793:0.654093:0.000000 2:@0.350793:0.684506:0.359776:0.684506:0.359776:0.668073:0.350793:0.668073:0.000000 (:@0.363365:0.676768:0.372201:0.676768:0.372201:0.660334:0.363365:0.660334:0.000000:0.000000 BC :@0.372108:0.676768:0.394013:0.676768:0.394013:0.660362:0.372108:0.660362:0.000000:0.000000:0.000000 2 :@0.393958:0.676213:0.413801:0.676213:0.413801:0.662498:0.393958:0.662498:0.000000:0.000000 AB:@0.413709:0.676768:0.432355:0.676768:0.432355:0.660362:0.413709:0.660362:0.000000:0.000000 ):@0.432300:0.676768:0.437178:0.676768:0.437178:0.660334:0.432300:0.660334:0.000000 Así,:@0.119800:0.707708:0.144109:0.707708:0.144109:0.691274:0.119800:0.691274:0.000000:0.000000:0.000000:0.000000 :@0.119811:0.743204:0.123843:0.743204:0.123843:0.726770:0.119811:0.726770:0.000000 AO:@0.128935:0.743204:0.150305:0.743204:0.150305:0.726798:0.128935:0.726798:0.000000:0.000000 (:@0.150250:0.743204:0.198468:0.743204:0.198468:0.726770:0.150250:0.726770:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.154208:0.742649:0.169541:0.742649:0.169541:0.728934:0.154208:0.728934:0.000000 1:@0.177060:0.736963:0.186043:0.736963:0.186043:0.720530:0.177060:0.720530:0.000000 2:@0.177060:0.750943:0.186043:0.750943:0.186043:0.734509:0.177060:0.734509:0.000000 AB:@0.198376:0.743204:0.217022:0.743204:0.217022:0.726798:0.198376:0.726798:0.000000:0.000000 :@0.216967:0.743204:0.220998:0.743204:0.220998:0.726770:0.216967:0.726770:0.000000 1 :@0.220925:0.742649:0.240768:0.742649:0.240768:0.728934:0.220925:0.728934:0.000000:0.000000 BC:@0.240676:0.743204:0.259341:0.743204:0.259341:0.726798:0.240676:0.726798:0.000000:0.000000 ):@0.259285:0.743204:0.264163:0.743204:0.264163:0.726770:0.259285:0.726770:0.000000 :@0.119811:0.778703:0.123843:0.778703:0.123843:0.762269:0.119811:0.762269:0.000000 BG:@0.128935:0.778703:0.148594:0.778703:0.148594:0.762297:0.128935:0.762297:0.000000:0.000000 (:@0.148538:0.778703:0.196756:0.778702:0.196756:0.762268:0.148538:0.762269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.152496:0.778148:0.167829:0.778148:0.167829:0.764433:0.152496:0.764433:0.000000 1:@0.175348:0.772461:0.184331:0.772461:0.184331:0.756027:0.175348:0.756027:0.000000 2:@0.175348:0.786440:0.184331:0.786440:0.184331:0.770006:0.175348:0.770006:0.000000 BC:@0.196664:0.778702:0.215329:0.778702:0.215329:0.762296:0.196664:0.762296:0.000000:0.000000 :@0.215274:0.778702:0.219305:0.778702:0.219305:0.762268:0.215274:0.762268:0.000000 1 :@0.219231:0.778147:0.239074:0.778147:0.239074:0.764431:0.219231:0.764431:0.000000:0.000000 AB:@0.238982:0.778702:0.257629:0.778702:0.257629:0.762296:0.238982:0.762296:0.000000:0.000000 ):@0.257574:0.778702:0.262451:0.778702:0.262451:0.762268:0.257574:0.762268:0.000000 Sumando miembro a miembro, resulta que :@0.119814:0.809642:0.488691:0.809642:0.488691:0.793208:0.119814:0.793208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 BC:@0.493444:0.809642:0.512790:0.809642:0.512790:0.793236:0.493444:0.793236:0.000000:0.000000 :@0.513398:0.809642:0.517429:0.809642:0.517429:0.793208:0.513398:0.793208:0.000000 5:@0.522233:0.809087:0.537566:0.809087:0.537566:0.795371:0.522233:0.795371:0.000000 AO :@0.538413:0.809642:0.575723:0.809642:0.575723:0.793208:0.538413:0.793208:0.000000:0.000000:0.000000:0.000000 1:@0.580529:0.809087:0.595862:0.809087:0.595862:0.795371:0.580529:0.795371:0.000000 :@0.596709:0.809642:0.600740:0.809642:0.600740:0.793208:0.596709:0.793208:0.000000 BG:@0.605563:0.809642:0.625903:0.809642:0.625903:0.793236:0.605563:0.793236:0.000000:0.000000 y como :@0.626510:0.809642:0.702900:0.809642:0.702900:0.793208:0.626510:0.793208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AO:@0.707686:0.809642:0.729738:0.809642:0.729738:0.793236:0.707686:0.793236:0.000000:0.000000 :@0.730345:0.809642:0.734377:0.809642:0.734377:0.793208:0.730345:0.793208:0.000000 5:@0.739199:0.809087:0.754533:0.809087:0.754533:0.795371:0.739199:0.795371:0.000000 OC, se sigue que :@0.755379:0.809642:0.913608:0.809642:0.913608:0.793208:0.755379:0.793208:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 :@0.909540:0.809642:0.913571:0.809642:0.913571:0.793208:0.909540:0.793208:0.000000 BC:@0.119832:0.826283:0.138497:0.826283:0.138497:0.809877:0.119832:0.809877:0.000000:0.000000 = :@0.138442:0.826283:0.157309:0.826283:0.157309:0.809850:0.138442:0.809850:0.000000:0.000000:0.000000 BG:@0.157217:0.826283:0.176876:0.826283:0.176876:0.809877:0.157217:0.809877:0.000000:0.000000 :@0.176821:0.826283:0.200032:0.826283:0.200032:0.809850:0.176821:0.809850:0.000000:0.000000:0.000000 1:@0.180760:0.825729:0.196093:0.825729:0.196093:0.812013:0.180760:0.812013:0.000000 OC:@0.199940:0.826283:0.221643:0.826283:0.221643:0.809877:0.199940:0.809877:0.000000:0.000000 . Pero :@0.221587:0.826283:0.265089:0.826283:0.265089:0.809850:0.221587:0.809850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 BO:@0.264997:0.826283:0.285632:0.826283:0.285632:0.809877:0.264997:0.809877:0.000000:0.000000 :@0.285571:0.826283:0.308783:0.826283:0.308783:0.809850:0.285571:0.809850:0.000000:0.000000:0.000000 5:@0.289510:0.825729:0.304843:0.825729:0.304843:0.812013:0.289510:0.812013:0.000000 CO:@0.308690:0.826283:0.329932:0.826283:0.329932:0.809877:0.308690:0.809877:0.000000:0.000000 BC, con lo que :@0.329877:0.826283:0.461268:0.826283:0.461268:0.809850:0.329877:0.809850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 1:@0.333816:0.825729:0.349150:0.825729:0.349150:0.812013:0.333816:0.812013:0.000000 BG:@0.461139:0.826283:0.480798:0.826283:0.480798:0.809877:0.461139:0.809877:0.000000:0.000000 :@0.480743:0.826283:0.503955:0.826283:0.503955:0.809850:0.480743:0.809850:0.000000:0.000000:0.000000 1:@0.484682:0.825729:0.500015:0.825729:0.500015:0.812013:0.484682:0.812013:0.000000 OC:@0.503863:0.826283:0.525565:0.826283:0.525565:0.809877:0.503863:0.809877:0.000000:0.000000 :@0.525510:0.826283:0.548721:0.826283:0.548721:0.809850:0.525510:0.809850:0.000000:0.000000:0.000000 5:@0.529449:0.825729:0.544782:0.825729:0.544782:0.812013:0.529449:0.812013:0.000000 BO:@0.548629:0.826283:0.569264:0.826283:0.569264:0.809877:0.548629:0.809877:0.000000:0.000000 :@0.569208:0.826283:0.592420:0.826283:0.592420:0.809850:0.569208:0.809850:0.000000:0.000000:0.000000 1:@0.573147:0.825729:0.588481:0.825729:0.588481:0.812013:0.573147:0.812013:0.000000 OC:@0.592328:0.826283:0.614030:0.826283:0.614030:0.809877:0.592328:0.809877:0.000000:0.000000 y, por la ley cancelativa, se obtiene :@0.613975:0.826283:0.870852:0.826283:0.870852:0.809850:0.613975:0.809850:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 BG:@0.870609:0.826283:0.890268:0.826283:0.890268:0.809877:0.870609:0.809877:0.000000:0.000000 :@0.890212:0.826283:0.913516:0.826283:0.913516:0.809850:0.890212:0.809850:0.000000:0.000000:0.000000 5:@0.894152:0.825729:0.909485:0.825729:0.909485:0.812013:0.894152:0.812013:0.000000 BO:@0.119777:0.842925:0.140411:0.842925:0.140411:0.826519:0.119777:0.826519:0.000000:0.000000 . Luego, , es decir que es el punto medio de las diagonales :@0.140356:0.842925:0.625859:0.842925:0.625859:0.826491:0.140356:0.826491:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 G:@0.200217:0.842925:0.211114:0.842925:0.211114:0.826519:0.200217:0.826519:0.000000 5:@0.214998:0.842371:0.230331:0.842371:0.230331:0.828655:0.214998:0.828655:0.000000 O:@0.234196:0.842925:0.246069:0.842925:0.246069:0.826519:0.234196:0.826519:0.000000 O:@0.345008:0.842925:0.356881:0.842925:0.356881:0.826519:0.345008:0.826519:0.000000 3:@0.625535:0.843508:0.629621:0.843508:0.629621:0.825854:0.625535:0.825854:0.000000 A, C:@0.629529:0.842925:0.655741:0.842925:0.655741:0.826519:0.629529:0.826519:0.000000:0.000000:0.000000:0.000000 4 3:@0.655704:0.843508:0.679707:0.843508:0.679707:0.825854:0.655704:0.825854:0.000000:0.000000:0.000000 y :@0.659698:0.842925:0.675713:0.842925:0.675713:0.826491:0.659698:0.826491:0.000000:0.000000:0.000000 B, D:@0.679615:0.842925:0.706129:0.842925:0.706129:0.826519:0.679615:0.826519:0.000000:0.000000:0.000000:0.000000 4:@0.706085:0.843508:0.710171:0.843508:0.710171:0.825854:0.706085:0.825854:0.000000 .:@0.710079:0.842925:0.713282:0.842925:0.713282:0.826491:0.710079:0.826491:0.000000 a. ¿Cuál es la condición de paralelismo del paralelogramo que tiene como vértices los puntos :@0.121235:0.873860:0.813915:0.873860:0.813915:0.857426:0.121235:0.857426:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 A, B, C, D:@0.813250:0.873860:0.872400:0.873860:0.872400:0.857454:0.813250:0.857454:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 ?:@0.872393:0.873860:0.879406:0.873860:0.879406:0.857426:0.872393:0.857426:0.000000 b. ¿Por qué se afirma que :@0.121235:0.912933:0.320123:0.912933:0.320123:0.896499:0.121235:0.896499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 AO:@0.319899:0.912933:0.341270:0.912933:0.341270:0.896526:0.319899:0.896526:0.000000:0.000000 (:@0.341214:0.912933:0.389436:0.912932:0.389436:0.896498:0.341214:0.896499:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000 5:@0.345172:0.912378:0.360505:0.912378:0.360505:0.898662:0.345172:0.898662:0.000000 1:@0.368029:0.906691:0.377012:0.906691:0.377012:0.890257:0.368029:0.890257:0.000000 2:@0.368029:0.920670:0.377012:0.920670:0.377012:0.904236:0.368029:0.904236:0.000000 AB:@0.389344:0.912932:0.407991:0.912932:0.407991:0.896526:0.389344:0.896526:0.000000:0.000000 :@0.407936:0.912932:0.431166:0.912932:0.431166:0.896498:0.407936:0.896498:0.000000:0.000000:0.000000 1:@0.411893:0.912377:0.427227:0.912377:0.427227:0.898661:0.411893:0.898661:0.000000 BC:@0.431092:0.912932:0.449757:0.912932:0.449757:0.896526:0.431092:0.896526:0.000000:0.000000 )?:@0.449702:0.912932:0.461519:0.912932:0.461519:0.896498:0.449702:0.896498:0.000000:0.000000 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