224:@0.031627:0.974518:0.062330:0.974518:0.062330:0.956333:0.031627:0.956333:0.000000:0.000000:0.000000
Geometría:@0.073089:0.043661:0.168070:0.043661:0.168070:0.024916:0.073089:0.024916:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
7.  Halla el valor del ángulo x si se sabe que las rectas :@0.073089:0.136836:0.489951:0.136836:0.489951:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 :@0.485772:0.136836:0.489674:0.136836:0.489674:0.120167:0.485772:0.120167:0.000000
m n:@0.103214:0.153478:0.143489:0.153478:0.143489:0.137072:0.103214:0.137072:0.000000:0.000000:0.000000
 y   son paralelas, y, además, que :@0.117756:0.153478:0.369127:0.153478:0.369127:0.136808:0.117756:0.136808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
α–β=:@0.368941:0.154061:0.415696:0.154061:0.415696:0.136406:0.368941:0.136406:0.000000:0.000000:0.000000:0.000000
62º.:@0.415604:0.153478:0.444613:0.153478:0.444613:0.136808:0.415604:0.136808:0.000000:0.000000:0.000000:0.000000
:@0.227715:0.253598:0.238877:0.253598:0.238877:0.237548:0.227715:0.237548:0.000000
:@0.251126:0.225319:0.262287:0.225319:0.262287:0.209270:0.251126:0.209270:0.000000
x:@0.229891:0.277262:0.237070:0.277262:0.237070:0.262978:0.229891:0.262978:0.000000
m:@0.430376:0.206655:0.445451:0.206655:0.445451:0.190942:0.430376:0.190942:0.000000
p:@0.306440:0.176062:0.316601:0.176062:0.316601:0.160349:0.306440:0.160349:0.000000
n:@0.435585:0.281959:0.445451:0.281959:0.445451:0.266247:0.435585:0.266247:0.000000
8.  Halla los valores de los ángulos  ,   si se sabe que :@0.073089:0.379372:0.489673:0.379372:0.489673:0.362702:0.073089:0.362702:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x y:@0.349614:0.379372:0.373046:0.379372:0.373046:0.362966:0.349614:0.362966:0.000000:0.000000:0.000000
las rectas   y   son paralelas.:@0.103196:0.396014:0.322840:0.396014:0.322840:0.379344:0.103196:0.379344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m n:@0.176438:0.396014:0.216713:0.396014:0.216713:0.379608:0.176438:0.379608:0.000000:0.000000:0.000000
4x:@0.240838:0.470961:0.256183:0.470961:0.256183:0.456677:0.240838:0.456677:0.000000:0.000000
m:@0.430376:0.449191:0.445451:0.449191:0.445451:0.433478:0.430376:0.433478:0.000000
p:@0.306440:0.418598:0.316601:0.418598:0.316601:0.402885:0.306440:0.402885:0.000000
n:@0.435585:0.524495:0.445451:0.524495:0.445451:0.508782:0.435585:0.508782:0.000000
2x:@0.276675:0.497073:0.292020:0.497073:0.292020:0.482788:0.276675:0.482788:0.000000:0.000000
:@0.292020:0.497970:0.307353:0.497970:0.307353:0.480316:0.292020:0.480316:0.000000
32°:@0.307353:0.497388:0.330731:0.497388:0.330731:0.481675:0.307353:0.481675:0.000000:0.000000:0.000000
y:@0.272334:0.526385:0.279697:0.526385:0.279697:0.512101:0.272334:0.512101:0.000000
:@0.279697:0.527283:0.288901:0.527283:0.288901:0.509628:0.279697:0.509628:0.000000
14°:@0.290005:0.526700:0.315592:0.526700:0.315592:0.510988:0.290005:0.510988:0.000000:0.000000:0.000000
x:@0.122544:0.583113:0.129999:0.583113:0.129999:0.566707:0.122544:0.566707:0.000000
       :@0.265562:0.594545:0.293339:0.594545:0.293339:0.578832:0.265562:0.578832:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.301908:0.583112:0.309382:0.583112:0.309382:0.566706:0.301908:0.566706:0.000000
9.  Halla el valor del ángulo   si sabe que las rectas  :@0.073089:0.621908:0.489693:0.621908:0.489693:0.605238:0.073089:0.605238:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.303411:0.621908:0.310866:0.621908:0.310866:0.605502:0.303411:0.605502:0.000000
m n :@0.103233:0.638550:0.146747:0.638550:0.146747:0.622144:0.103233:0.622144:0.000000:0.000000:0.000000:0.000000
 y  son paralelas.:@0.117774:0.638550:0.249064:0.638550:0.249064:0.621880:0.117774:0.621880:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.225194:0.693791:0.232372:0.693791:0.232372:0.679506:0.225194:0.679506:0.000000
x:@0.325881:0.693791:0.333060:0.693791:0.333060:0.679506:0.325881:0.679506:0.000000
m:@0.430376:0.691727:0.445451:0.691727:0.445451:0.676014:0.430376:0.676014:0.000000
p:@0.308391:0.791675:0.318552:0.791675:0.318552:0.775962:0.308391:0.775962:0.000000
q:@0.337843:0.660218:0.347819:0.660218:0.347819:0.644505:0.337843:0.644505:0.000000
n:@0.435585:0.767017:0.445451:0.767017:0.445451:0.751304:0.435585:0.751304:0.000000
70°:@0.267418:0.784859:0.290795:0.784859:0.290795:0.769146:0.267418:0.769146:0.000000:0.000000:0.000000
10.  Se sabe que las rectas   y  son paralelas, halla el :@0.514231:0.136836:0.930679:0.136836:0.930679:0.120167:0.514231:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m  n:@0.717347:0.136836:0.759002:0.136836:0.759002:0.120153:0.717347:0.120153:0.000000:0.000000:0.000000:0.000000
valor del ángulo   Sugerencia: trazar una recta :@0.544337:0.153478:0.930843:0.153478:0.930843:0.136808:0.544337:0.136808:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x.:@0.682594:0.153478:0.694853:0.153478:0.694853:0.136795:0.682594:0.136795:0.000000:0.000000
auxiliar, paralela a   y  , que pase por el punto  .:@0.544337:0.170120:0.914783:0.170120:0.914783:0.153450:0.544337:0.153450:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
m n:@0.682428:0.170120:0.723292:0.170120:0.723292:0.153436:0.682428:0.153436:0.000000:0.000000:0.000000
A:@0.901161:0.170120:0.911046:0.170120:0.911046:0.153714:0.901161:0.153714:0.000000
108°:@0.663345:0.223075:0.692763:0.223075:0.692763:0.208791:0.663345:0.208791:0.000000:0.000000:0.000000:0.000000
122°:@0.695407:0.306940:0.724825:0.306940:0.724825:0.292655:0.695407:0.292655:0.000000:0.000000:0.000000:0.000000
x°:@0.695223:0.254694:0.707321:0.254694:0.707321:0.240410:0.695223:0.240410:0.000000:0.000000
A:@0.646343:0.254694:0.656132:0.254694:0.656132:0.240410:0.646343:0.240410:0.000000
m:@0.871517:0.223298:0.886593:0.223298:0.886593:0.207585:0.871517:0.207585:0.000000
p:@0.774971:0.191595:0.785132:0.191595:0.785132:0.175883:0.774971:0.175883:0.000000
q:@0.774695:0.322178:0.784672:0.322178:0.784672:0.306466:0.774695:0.306466:0.000000
n:@0.876708:0.298589:0.886575:0.298589:0.886575:0.282876:0.876708:0.282876:0.000000
11.  Demuestra que, en un paralelogramo, los ángulos :@0.514231:0.396014:0.930723:0.396014:0.930723:0.379344:0.514231:0.379344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
opuestos son congruentes.:@0.544355:0.412656:0.748851:0.412656:0.748851:0.395986:0.544355:0.395986:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.645801:0.440180:0.658090:0.440180:0.658090:0.421995:0.645801:0.421995:0.000000
B:@0.780244:0.562875:0.791128:0.562875:0.791128:0.544690:0.780244:0.544690:0.000000
C:@0.847300:0.440180:0.858947:0.440180:0.858947:0.421995:0.847300:0.421995:0.000000
D:@0.574382:0.562875:0.587756:0.562875:0.587756:0.544690:0.574382:0.544690:0.000000
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