231:@0.937671:0.974518:0.968375:0.974518:0.968375:0.956333:0.937671:0.956333:0.000000:0.000000:0.000000
Pensamiento espacial:@0.721207:0.043660:0.914624:0.043660:0.914624:0.024915:0.721207:0.024915:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 5:@0.073089:0.136836:0.149461:0.136836:0.149461:0.120167:0.073089:0.120167:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El ángulo mayor de un triángulo es el triple del menor y el ángulo mediano es el doble del menor. ¿Cuál es la medida :@0.073089:0.171340:0.931618:0.171340:0.931618:0.155628:0.073089:0.155628:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
de los ángulos interiores del triángulo?:@0.073089:0.187982:0.353514:0.187982:0.353514:0.172269:0.073089:0.172269:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Gráfica 5.20 triángulo escaleno con ángulos interior:@0.108670:0.232014:0.497619:0.232014:0.497619:0.215344:0.108670:0.215344:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.120461:0.420803:0.132812:0.420803:0.132812:0.402526:0.120461:0.402526:0.000000
C:@0.226555:0.296000:0.238260:0.296000:0.238260:0.277724:0.226555:0.277724:0.000000
3:@0.224739:0.323993:0.234587:0.323993:0.234587:0.306765:0.224739:0.306765:0.000000
x:@0.234587:0.323993:0.242761:0.323993:0.242761:0.306005:0.234587:0.306005:0.000000
x:@0.441186:0.402146:0.449359:0.402146:0.449359:0.384159:0.441186:0.384159:0.000000
2:@0.150511:0.401021:0.160360:0.401021:0.160360:0.383794:0.150511:0.383794:0.000000
x:@0.160360:0.401021:0.168533:0.401021:0.168533:0.383034:0.160360:0.383034:0.000000
Si el ángulo menor tiene una medida  , entonces::@0.539897:0.262282:0.897819:0.262282:0.897819:0.246569:0.539897:0.246569:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.812711:0.262282:0.820166:0.262282:0.820166:0.245876:0.812711:0.245876:0.000000
El ángulo mediano mide 2:@0.539879:0.282501:0.731222:0.282501:0.731222:0.266789:0.539879:0.266789:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.730983:0.282501:0.738438:0.282501:0.738438:0.266095:0.730983:0.266095:0.000000
El ángulo mayor mide 3:@0.539879:0.302721:0.711990:0.302721:0.711990:0.287009:0.539879:0.287009:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.711784:0.302721:0.719239:0.302721:0.719239:0.286315:0.711784:0.286315:0.000000
La suma de los ángulos interiores es 180º.:@0.539879:0.322941:0.840394:0.322941:0.840394:0.307228:0.539879:0.307228:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Luego, podemos escribir que::@0.539879:0.343161:0.754633:0.343161:0.754633:0.327448:0.539879:0.327448:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.666318:0.363381:0.673773:0.363381:0.673773:0.346975:0.666318:0.346975:0.000000
+ + =:@0.673700:0.363963:0.756514:0.363963:0.756514:0.346309:0.673700:0.346309:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.690045:0.363381:0.699028:0.363381:0.699028:0.347668:0.690045:0.347668:0.000000
x:@0.700059:0.363381:0.707514:0.363381:0.707514:0.346975:0.700059:0.346975:0.000000
3:@0.723786:0.363381:0.732769:0.363381:0.732769:0.347668:0.723786:0.347668:0.000000
x:@0.733799:0.363381:0.741254:0.363381:0.741254:0.346975:0.733799:0.346975:0.000000
180º:@0.757526:0.363381:0.793770:0.363381:0.793770:0.347668:0.757526:0.347668:0.000000:0.000000:0.000000:0.000000
6:@0.695052:0.383601:0.704035:0.383601:0.704035:0.367888:0.695052:0.367888:0.000000
x:@0.705066:0.383601:0.712521:0.383601:0.712521:0.367195:0.705066:0.367195:0.000000
=:@0.712447:0.384183:0.727780:0.384183:0.727780:0.366529:0.712447:0.366529:0.000000
180º:@0.728793:0.383601:0.765036:0.383601:0.765036:0.367888:0.728793:0.367888:0.000000:0.000000:0.000000:0.000000
x:@0.705066:0.403820:0.712521:0.403820:0.712521:0.387414:0.705066:0.387414:0.000000
=:@0.712447:0.404403:0.727780:0.404403:0.727780:0.386749:0.712447:0.386749:0.000000
30º:@0.728793:0.403820:0.755023:0.403820:0.755023:0.388108:0.728793:0.388108:0.000000:0.000000:0.000000
Por lo tanto, los ángulos miden 30º, 60º y 90º.:@0.539879:0.424040:0.866457:0.424040:0.866457:0.408328:0.539879:0.408328:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 6:@0.073071:0.494491:0.149443:0.494491:0.149443:0.477821:0.073071:0.477821:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Encuentra la medida de los ángulos que faltan en la figura.:@0.073071:0.528995:0.496548:0.528995:0.496548:0.513282:0.073071:0.513282:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Gráfica 5.19 triángulo rectángulo con ángulos interior:@0.097129:0.579863:0.502019:0.579863:0.502019:0.563194:0.097129:0.563194:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
A:@0.099589:0.829941:0.110854:0.829941:0.110854:0.813271:0.099589:0.813271:0.000000
B:@0.116045:0.616135:0.126021:0.616135:0.126021:0.599465:0.116045:0.599465:0.000000
D:@0.086519:0.712519:0.098779:0.712519:0.098779:0.695849:0.086519:0.695849:0.000000
C:@0.463482:0.829941:0.474158:0.829941:0.474158:0.813271:0.463482:0.813271:0.000000
z:@0.408057:0.810872:0.415936:0.810872:0.415936:0.794203:0.408057:0.794203:0.000000
y:@0.113762:0.702035:0.122432:0.702035:0.122432:0.685365:0.113762:0.685365:0.000000
x:@0.113762:0.639073:0.122285:0.639073:0.122285:0.622403:0.113762:0.622403:0.000000
74°:@0.108958:0.731324:0.133697:0.731324:0.133697:0.714655:0.108958:0.714655:0.000000:0.000000:0.000000
15°:@0.360695:0.781042:0.385435:0.781042:0.385435:0.764372:0.360695:0.764372:0.000000:0.000000:0.000000
En el punto   tenemos que:@0.532782:0.567321:0.732751:0.567321:0.732751:0.551609:0.532782:0.551609:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
D:@0.620345:0.567321:0.631868:0.567321:0.631868:0.550915:0.620345:0.550915:0.000000
74º:@0.532764:0.587541:0.556785:0.587541:0.556785:0.571829:0.532764:0.571829:0.000000:0.000000:0.000000
+∡ =:@0.556693:0.588124:0.609908:0.588124:0.609908:0.570469:0.556693:0.570469:0.000000:0.000000:0.000000:0.000000
y:@0.587175:0.587541:0.594649:0.587541:0.594649:0.571135:0.587175:0.571135:0.000000
180º por ser adyascentes.:@0.609816:0.587541:0.792954:0.587541:0.792954:0.571829:0.609816:0.571829:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Luego, :@0.532764:0.607761:0.585651:0.607761:0.585651:0.592048:0.532764:0.592048:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∡ =:@0.585537:0.608344:0.623511:0.608344:0.623511:0.590689:0.585537:0.590689:0.000000:0.000000:0.000000
y:@0.600778:0.607761:0.608252:0.607761:0.608252:0.591355:0.600778:0.591355:0.000000
106º:@0.623419:0.607761:0.656350:0.607761:0.656350:0.592048:0.623419:0.592048:0.000000:0.000000:0.000000:0.000000
En el :@0.532745:0.627981:0.571713:0.627981:0.571713:0.612268:0.532745:0.612268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∆:@0.571603:0.628563:0.583881:0.628563:0.583881:0.610909:0.571603:0.610909:0.000000
CDB:@0.583789:0.627981:0.613903:0.627981:0.613903:0.611575:0.583789:0.611575:0.000000:0.000000:0.000000
 tenemos que :@0.613848:0.627981:0.718835:0.627981:0.718835:0.612268:0.613848:0.612268:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∡ +∡ +:@0.532745:0.648783:0.608583:0.648783:0.608583:0.631129:0.532745:0.631129:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.547986:0.648201:0.555441:0.648201:0.555441:0.631795:0.547986:0.631795:0.000000
y:@0.585850:0.648201:0.593324:0.648201:0.593324:0.631795:0.585850:0.631795:0.000000
15º 180º:@0.608491:0.648201:0.680592:0.648201:0.680592:0.632488:0.608491:0.632488:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.632421:0.648783:0.647754:0.648783:0.647754:0.631129:0.632421:0.631129:0.000000
Como :@0.532727:0.668421:0.581499:0.668421:0.581499:0.652708:0.532727:0.652708:0.000000:0.000000:0.000000:0.000000:0.000000
∡ =:@0.581396:0.669003:0.619370:0.669003:0.619370:0.651349:0.581396:0.651349:0.000000:0.000000:0.000000
y:@0.596637:0.668421:0.604110:0.668421:0.604110:0.652014:0.596637:0.652014:0.000000
106º:@0.619278:0.668421:0.652208:0.668421:0.652208:0.652708:0.619278:0.652708:0.000000:0.000000:0.000000:0.000000
Al reemplazar, obtenemos: :@0.532727:0.688640:0.730049:0.688640:0.730049:0.672928:0.532727:0.672928:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∡ +:@0.532727:0.709443:0.570683:0.709443:0.570683:0.691788:0.532727:0.691788:0.000000:0.000000:0.000000
x:@0.547968:0.708860:0.555423:0.708860:0.555423:0.692454:0.547968:0.692454:0.000000
106º 15º 180º:@0.570591:0.708860:0.690753:0.708860:0.690753:0.693148:0.570591:0.693148:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.603411:0.709443:0.618744:0.709443:0.618744:0.691788:0.603411:0.691788:0.000000
=:@0.642581:0.709443:0.657915:0.709443:0.657915:0.691788:0.642581:0.691788:0.000000
De donde: :@0.532708:0.729080:0.612865:0.729080:0.612865:0.713367:0.532708:0.713367:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∡ =:@0.612725:0.729662:0.650681:0.729662:0.650681:0.712008:0.612725:0.712008:0.000000:0.000000:0.000000
x:@0.627966:0.729080:0.635421:0.729080:0.635421:0.712674:0.627966:0.712674:0.000000
59º:@0.650588:0.729080:0.674610:0.729080:0.674610:0.713367:0.650588:0.713367:0.000000:0.000000:0.000000
En el :@0.532690:0.749300:0.571658:0.749300:0.571658:0.733587:0.532690:0.733587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∆:@0.571548:0.749882:0.583825:0.749882:0.583825:0.732228:0.571548:0.732228:0.000000
CAB:@0.583733:0.749300:0.612209:0.749300:0.612209:0.732894:0.583733:0.732894:0.000000:0.000000:0.000000
 tenemos que:@0.612154:0.749300:0.713111:0.749300:0.713111:0.733587:0.612154:0.733587:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∡ +:@0.532690:0.770102:0.570646:0.770102:0.570646:0.752448:0.532690:0.752448:0.000000:0.000000:0.000000
x:@0.547931:0.769520:0.555386:0.769520:0.555386:0.753114:0.547931:0.753114:0.000000
90º:@0.570554:0.769520:0.594575:0.769520:0.594575:0.753807:0.570554:0.753807:0.000000:0.000000:0.000000
+∡ +:@0.594483:0.770102:0.647459:0.770102:0.647459:0.752448:0.594483:0.752448:0.000000:0.000000:0.000000:0.000000
z:@0.624966:0.769520:0.632200:0.769520:0.632200:0.753114:0.624966:0.753114:0.000000
15º 180º:@0.647367:0.769520:0.719468:0.769520:0.719468:0.753807:0.647367:0.753807:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.671297:0.770102:0.686630:0.770102:0.686630:0.752448:0.671297:0.752448:0.000000
Pero :@0.532672:0.789740:0.569105:0.789740:0.569105:0.774027:0.532672:0.774027:0.000000:0.000000:0.000000:0.000000:0.000000
∡ =:@0.569008:0.790322:0.606963:0.790322:0.606963:0.772668:0.569008:0.772668:0.000000:0.000000:0.000000
x:@0.584249:0.789740:0.591704:0.789740:0.591704:0.773333:0.584249:0.773333:0.000000
59º:@0.606871:0.789740:0.630893:0.789740:0.630893:0.774027:0.606871:0.774027:0.000000:0.000000:0.000000
Luego: :@0.532653:0.809959:0.585953:0.809959:0.585953:0.794247:0.532653:0.794247:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
59º 90º:@0.532653:0.830179:0.595845:0.830179:0.595845:0.814466:0.532653:0.814466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+:@0.556583:0.830762:0.571916:0.830762:0.571916:0.813107:0.556583:0.813107:0.000000
+∡ +:@0.595753:0.830762:0.648729:0.830762:0.648729:0.813107:0.595753:0.813107:0.000000:0.000000:0.000000:0.000000
z:@0.626236:0.830179:0.633470:0.830179:0.633470:0.813773:0.626236:0.813773:0.000000
15º 180º:@0.648637:0.830179:0.720739:0.830179:0.720739:0.814466:0.648637:0.814466:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.672567:0.830762:0.687900:0.830762:0.687900:0.813107:0.672567:0.813107:0.000000
De donde: :@0.532653:0.850399:0.612809:0.850399:0.612809:0.834686:0.532653:0.834686:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∡ =:@0.612670:0.850981:0.650404:0.850981:0.650404:0.833327:0.612670:0.833327:0.000000:0.000000:0.000000
z:@0.627911:0.850399:0.635145:0.850399:0.635145:0.833993:0.627911:0.833993:0.000000
16º:@0.650312:0.850399:0.674334:0.850399:0.674334:0.834686:0.650312:0.834686:0.000000:0.000000:0.000000
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