162:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000
 Vectores geométricos en el plano:@0.073089:0.043661:0.371606:0.043661:0.371606:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Actividad indagatoria:@0.085363:0.139204:0.248724:0.139204:0.248724:0.122534:0.085363:0.122534:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4.  Demuestren que la mediana de la base de un triángulo isósceles es perpendicular a la base. Sea  un :@0.087319:0.163996:0.910254:0.163996:0.910254:0.147327:0.087319:0.147327:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T :@0.873522:0.163996:0.885045:0.163996:0.885045:0.147590:0.873522:0.147590:0.000000:0.000000
triángulo isósceles, denotemos con  ,  ,   sus vértices. La base de   es el segmento de recta  ,   y la :@0.117444:0.180638:0.910300:0.180638:0.910300:0.163969:0.117444:0.163969:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A B C:@0.396922:0.180638:0.443106:0.180638:0.443106:0.164232:0.396922:0.164232:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.634467:0.180638:0.642585:0.180638:0.642585:0.164232:0.634467:0.164232:0.000000
3:@0.838788:0.181221:0.842874:0.181221:0.842874:0.163567:0.838788:0.163567:0.000000
A B:@0.842966:0.180638:0.870467:0.180638:0.870467:0.164232:0.842966:0.164232:0.000000:0.000000:0.000000
4:@0.870540:0.181221:0.874627:0.181221:0.874627:0.163567:0.870540:0.163567:0.000000
mediana a la base  ,   es el segmento  ,  , donde   es el punto medio de  ,  .:@0.117463:0.197280:0.722491:0.197280:0.722491:0.180611:0.117463:0.180611:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.256843:0.197863:0.260929:0.197863:0.260929:0.180208:0.256843:0.180208:0.000000
A B:@0.260837:0.197280:0.287049:0.197280:0.287049:0.180874:0.260837:0.180874:0.000000:0.000000:0.000000
4:@0.286975:0.197863:0.291062:0.197863:0.291062:0.180208:0.286975:0.180208:0.000000
3:@0.412899:0.197863:0.416986:0.197863:0.416986:0.180208:0.412899:0.180208:0.000000
P C:@0.416894:0.197280:0.443050:0.197280:0.443050:0.180874:0.416894:0.180874:0.000000:0.000000:0.000000
4:@0.442977:0.197863:0.447063:0.197863:0.447063:0.180208:0.442977:0.180208:0.000000
P:@0.508267:0.197280:0.517029:0.197280:0.517029:0.180874:0.508267:0.180874:0.000000
3:@0.684554:0.197863:0.688640:0.197863:0.688640:0.180208:0.684554:0.180208:0.000000
A B:@0.688548:0.197280:0.714760:0.197280:0.714760:0.180874:0.688548:0.180874:0.000000:0.000000:0.000000
4:@0.714686:0.197863:0.718773:0.197863:0.718773:0.180208:0.714686:0.180208:0.000000
En la Figura 3.12. se ilustra el triángulo isósceles   con sus vértices  ,  ,   y el punto medio P de  ,  , base del :@0.117444:0.238940:0.910411:0.238940:0.910411:0.222506:0.117444:0.222506:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.462765:0.238940:0.470882:0.238940:0.470882:0.222534:0.462765:0.222534:0.000000
A B C:@0.593603:0.238940:0.636327:0.238940:0.636327:0.222534:0.593603:0.222534:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.804863:0.239523:0.808950:0.239523:0.808950:0.221868:0.804863:0.221868:0.000000
A B:@0.808858:0.238940:0.834628:0.238940:0.834628:0.222534:0.808858:0.222534:0.000000:0.000000:0.000000
4:@0.834554:0.239523:0.838641:0.239523:0.838641:0.221868:0.834554:0.221868:0.000000
triángulo  . En la Figura 3.13. se muestra el triángulo   y los vectores AP, PB, PC, AB, AC y BC.:@0.117408:0.255582:0.772702:0.255582:0.772702:0.239148:0.117408:0.239148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
T:@0.187429:0.255582:0.195546:0.255582:0.195546:0.239176:0.187429:0.239176:0.000000
T:@0.496303:0.255582:0.504420:0.255582:0.504420:0.239176:0.496303:0.239176:0.000000
Figura 3.13:@0.460592:0.619525:0.539405:0.619525:0.539405:0.603091:0.460592:0.603091:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.417635:0.582053:0.427519:0.582053:0.427519:0.565647:0.417635:0.565647:0.000000
P:@0.503930:0.600860:0.516586:0.600860:0.516586:0.577162:0.503930:0.577162:0.000000
B:@0.592641:0.582053:0.601476:0.582053:0.601476:0.565647:0.592641:0.565647:0.000000
C:@0.502703:0.474450:0.512606:0.474450:0.512606:0.458044:0.502703:0.458044:0.000000
Figura 3.12:@0.460736:0.440373:0.539549:0.440373:0.539549:0.423939:0.460736:0.423939:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.412010:0.402908:0.421895:0.402908:0.421895:0.386502:0.412010:0.386502:0.000000
T:@0.462391:0.339197:0.470509:0.339197:0.470509:0.322791:0.462391:0.322791:0.000000
P:@0.505630:0.415555:0.514392:0.415555:0.514392:0.399149:0.505630:0.399149:0.000000
B:@0.597924:0.402908:0.606759:0.402908:0.606759:0.386502:0.597924:0.386502:0.000000
C:@0.506440:0.293765:0.516343:0.293765:0.516343:0.277359:0.506440:0.277359:0.000000
Demuestren que que  ,      ,   es equivalente a     :@0.117440:0.665799:0.521808:0.665799:0.521808:0.649366:0.117440:0.649366:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.276663:0.666382:0.280749:0.666382:0.280749:0.648728:0.276663:0.648728:0.000000
A B:@0.280657:0.665799:0.306372:0.665799:0.306372:0.649393:0.280657:0.649393:0.000000:0.000000:0.000000
4:@0.306299:0.666382:0.310385:0.666382:0.310385:0.648728:0.306299:0.648728:0.000000
3:@0.330391:0.666382:0.334477:0.666382:0.334477:0.648728:0.330391:0.648728:0.000000
P C:@0.334385:0.665799:0.360045:0.665799:0.360045:0.649393:0.334385:0.649393:0.000000:0.000000:0.000000
4:@0.359971:0.666382:0.364058:0.666382:0.364058:0.648728:0.359971:0.648728:0.000000
AB PC:@0.489190:0.665799:0.540326:0.665799:0.540326:0.649393:0.489190:0.649393:0.000000:0.000000:0.000000:0.000000:0.000000
?:@0.511739:0.665661:0.517869:0.665661:0.517869:0.651612:0.511739:0.651612:0.000000
   0.:@0.540270:0.665799:0.575539:0.665799:0.575539:0.649366:0.540270:0.649366:0.000000:0.000000:0.000000:0.000000:0.000000
5:@0.544228:0.665245:0.559561:0.665245:0.559561:0.651529:0.544228:0.651529:0.000000
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