209:@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
DBA 7 (Ev. 1) Describe teoremas y argumenta su validez a través de diferentes recursos (software, tangram, papel, entre otros).:@0.085169:0.956075:0.744437:0.956075:0.744437:0.944647:0.085169:0.944647:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 7 (Ev. 2) Argumenta la relación pitagórica por medio de construcción, al utilizar material concreto. :@0.085169:0.968178:0.625701:0.968178:0.625701:0.956751:0.085169:0.956751:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
DBA 5 (Ev. 3 G. 9) Justifica procedimientos de medición a partir del teorema de Pitágoras y relaciones intra e interfigurales.:@0.085169:0.980281:0.724033:0.980281:0.724033:0.968854:0.085169:0.968854:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Observa la tabla. Para hallar el complemento a 90º, se le :@0.073089:0.136836:0.489656:0.136836:0.489656:0.121124:0.073089:0.121124:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resta el ángulo. Para hallar el suplemento a 180º, se le :@0.073089:0.153478:0.489835:0.153478:0.489835:0.137765:0.073089:0.137765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
resta el ángulo.:@0.073089:0.170120:0.182507:0.170120:0.182507:0.154407:0.073089:0.154407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ángulo:@0.113910:0.202421:0.169846:0.202421:0.169846:0.185752:0.113910:0.185752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Complemento:@0.224427:0.202421:0.334453:0.202421:0.334453:0.185752:0.224427:0.185752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Suplemento:@0.370305:0.202421:0.463694:0.202421:0.463694:0.185752:0.370305:0.185752:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
25º:@0.129851:0.222905:0.153872:0.222905:0.153872:0.207192:0.129851:0.207192:0.000000:0.000000:0.000000
65º:@0.267408:0.222905:0.291430:0.222905:0.291430:0.207192:0.267408:0.207192:0.000000:0.000000:0.000000
155º:@0.400511:0.222905:0.433442:0.222905:0.433442:0.207192:0.400511:0.207192:0.000000:0.000000:0.000000:0.000000
43º:@0.129833:0.243388:0.153854:0.243388:0.153854:0.227675:0.129833:0.227675:0.000000:0.000000:0.000000
47º:@0.267390:0.243388:0.291411:0.243388:0.291411:0.227675:0.267390:0.227675:0.000000:0.000000:0.000000
137º:@0.400493:0.243388:0.433423:0.243388:0.433423:0.227675:0.400493:0.227675:0.000000:0.000000:0.000000:0.000000
58º:@0.129814:0.263871:0.153817:0.263871:0.153817:0.248159:0.129814:0.248159:0.000000:0.000000:0.000000
32º:@0.267372:0.263871:0.291375:0.263871:0.291375:0.248159:0.267372:0.248159:0.000000:0.000000:0.000000
122º:@0.400474:0.263871:0.433387:0.263871:0.433387:0.248159:0.400474:0.248159:0.000000:0.000000:0.000000:0.000000
62º:@0.129814:0.284355:0.153817:0.284355:0.153817:0.268642:0.129814:0.268642:0.000000:0.000000:0.000000
28º:@0.267372:0.284355:0.291375:0.284355:0.291375:0.268642:0.267372:0.268642:0.000000:0.000000:0.000000
118º:@0.400474:0.284355:0.433387:0.284355:0.433387:0.268642:0.400474:0.268642:0.000000:0.000000:0.000000:0.000000
84º:@0.129814:0.304838:0.153817:0.304838:0.153817:0.289125:0.129814:0.289125:0.000000:0.000000:0.000000
6º:@0.271826:0.304838:0.286938:0.304838:0.286938:0.289125:0.271826:0.289125:0.000000:0.000000
96º:@0.404947:0.304838:0.428950:0.304838:0.428950:0.289125:0.404947:0.289125:0.000000:0.000000:0.000000
Ejemplo 1:@0.073046:0.333296:0.149418:0.333296:0.149418:0.316626:0.073046:0.316626:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Halla la medida de los ángulos dados:@0.073046:0.361379:0.342381:0.361379:0.342381:0.345666:0.073046:0.345666:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Gráfica 2.12 opuestos por el vértice:@0.146730:0.389462:0.412157:0.389462:0.412157:0.372792:0.146730:0.372792:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2:@0.256951:0.439481:0.265320:0.439481:0.265320:0.424842:0.256951:0.424842:0.000000
x:@0.266349:0.439481:0.273294:0.439481:0.273294:0.424196:0.266349:0.424196:0.000000
:@0.274323:0.440023:0.288609:0.440023:0.288609:0.423576:0.274323:0.423576:0.000000
2°:@0.289638:0.439481:0.304077:0.439481:0.304077:0.424842:0.289638:0.424842:0.000000:0.000000
3:@0.255116:0.499832:0.263485:0.499832:0.263485:0.485193:0.255116:0.485193:0.000000
x:@0.264514:0.499832:0.271459:0.499832:0.271459:0.484547:0.264514:0.484547:0.000000
:@0.272488:0.500375:0.281063:0.500375:0.281063:0.483927:0.272488:0.483927:0.000000
53°:@0.282092:0.499832:0.305930:0.499832:0.305930:0.485193:0.282092:0.485193:0.000000:0.000000:0.000000
A:@0.300596:0.466433:0.311092:0.466433:0.311092:0.450902:0.300596:0.450902:0.000000
B:@0.379518:0.443783:0.388813:0.443783:0.388813:0.428253:0.379518:0.428253:0.000000
C:@0.384800:0.522404:0.394746:0.522404:0.394746:0.506874:0.384800:0.506874:0.000000
D:@0.170210:0.523580:0.181631:0.523580:0.181631:0.508050:0.170210:0.508050:0.000000
E:@0.147744:0.425384:0.156181:0.425384:0.156181:0.409854:0.147744:0.409854:0.000000
De acuerdo con la gráfica, :@0.073089:0.556838:0.264486:0.556838:0.264486:0.541126:0.073089:0.541126:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∡:@0.264235:0.557421:0.279569:0.557421:0.279569:0.539767:0.264235:0.539767:0.000000
DAC:@0.279476:0.556838:0.310334:0.556838:0.310334:0.540432:0.279476:0.540432:0.000000:0.000000:0.000000
 y el :@0.310272:0.556838:0.342779:0.556838:0.342779:0.541126:0.310272:0.541126:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∡:@0.342632:0.557421:0.357965:0.557421:0.357965:0.539767:0.342632:0.539767:0.000000
EAB:@0.357873:0.556838:0.384564:0.556838:0.384564:0.540432:0.357873:0.540432:0.000000:0.000000:0.000000
 son opuestos :@0.384508:0.556838:0.489846:0.556838:0.489846:0.541126:0.384508:0.541126:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
por el vértice. Sabemos que esos ángulos son congruentes :@0.073076:0.573480:0.489755:0.573480:0.489755:0.557767:0.073076:0.557767:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(tienen la misma medida). Por consiguiente::@0.073076:0.590122:0.390623:0.590122:0.390623:0.574409:0.073076:0.574409:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.217739:0.618205:0.226721:0.618205:0.226721:0.602492:0.217739:0.602492:0.000000
x:@0.227752:0.618205:0.235207:0.618205:0.235207:0.601799:0.227752:0.601799:0.000000
–:@0.236238:0.618788:0.245441:0.618788:0.245441:0.601133:0.236238:0.601133:0.000000
53º 2:@0.246454:0.618205:0.299025:0.618205:0.299025:0.602492:0.246454:0.602492:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.273697:0.618788:0.289030:0.618788:0.289030:0.601133:0.273697:0.601133:0.000000
x:@0.300056:0.618205:0.307511:0.618205:0.307511:0.601799:0.300056:0.601799:0.000000
+:@0.308542:0.618788:0.323875:0.618788:0.323875:0.601133:0.308542:0.601133:0.000000
2º:@0.324887:0.618205:0.341104:0.618205:0.341104:0.602492:0.324887:0.602492:0.000000:0.000000
Restando 2  y sumando 53º a cada lado, obtenemos::@0.073076:0.646288:0.456576:0.646288:0.456576:0.630575:0.073076:0.630575:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.154178:0.646288:0.161633:0.646288:0.161633:0.629882:0.154178:0.629882:0.000000
3:@0.147607:0.674371:0.156590:0.674371:0.156590:0.658659:0.147607:0.658659:0.000000
x:@0.157620:0.674371:0.165075:0.674371:0.165075:0.657965:0.157620:0.657965:0.000000
–:@0.166106:0.674954:0.175310:0.674954:0.175310:0.657299:0.166106:0.657299:0.000000
53º 2:@0.176322:0.674371:0.222764:0.674371:0.222764:0.658659:0.176322:0.658659:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.203565:0.674954:0.212769:0.674954:0.212769:0.657299:0.203565:0.657299:0.000000
x:@0.223795:0.674371:0.231249:0.674371:0.231249:0.657965:0.223795:0.657965:0.000000
+:@0.232280:0.674954:0.247614:0.674954:0.247614:0.657299:0.232280:0.657299:0.000000
53º 2 +2º 2:@0.248626:0.674371:0.359143:0.674371:0.359143:0.658659:0.248626:0.658659:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.275869:0.674954:0.291202:0.674954:0.291202:0.657299:0.275869:0.657299:0.000000
x:@0.302228:0.674371:0.309683:0.674371:0.309683:0.657965:0.302228:0.657965:0.000000
–:@0.339944:0.674954:0.349148:0.674954:0.349148:0.657299:0.339944:0.657299:0.000000
x:@0.360174:0.674371:0.367629:0.674371:0.367629:0.657965:0.360174:0.657965:0.000000
+:@0.368660:0.674954:0.383993:0.674954:0.383993:0.657299:0.368660:0.657299:0.000000
53º:@0.385005:0.674371:0.411236:0.674371:0.411236:0.658659:0.385005:0.658659:0.000000:0.000000:0.000000
x:@0.253890:0.702454:0.261345:0.702454:0.261345:0.686048:0.253890:0.686048:0.000000
=:@0.262376:0.703037:0.277709:0.703037:0.277709:0.685383:0.262376:0.685383:0.000000
55º:@0.278722:0.702454:0.304952:0.702454:0.304952:0.686742:0.278722:0.686742:0.000000:0.000000:0.000000
Luego, cada ángulo mide 112º:@0.073076:0.730537:0.294169:0.730537:0.294169:0.714825:0.073076:0.714825:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 2:@0.073076:0.758621:0.149448:0.758621:0.149448:0.741951:0.073076:0.741951:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Un ángulo es 12º mayor que el doble de su complemento. :@0.073076:0.786704:0.489949:0.786704:0.489949:0.770991:0.073076:0.770991:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Halla la medida del ángulo.:@0.073076:0.803345:0.269310:0.803345:0.269310:0.787633:0.073076:0.787633:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Sea   la medida del ángulo.:@0.073076:0.831429:0.270560:0.831429:0.270560:0.815716:0.073076:0.815716:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.102693:0.831429:0.110148:0.831429:0.110148:0.815022:0.102693:0.815022:0.000000
El complemento del ángulo es 90º:@0.073058:0.859512:0.325419:0.859512:0.325419:0.843799:0.073058:0.843799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.326249:0.860094:0.335453:0.860094:0.335453:0.842440:0.326249:0.842440:0.000000
x:@0.336465:0.859512:0.343920:0.859512:0.343920:0.843106:0.336465:0.843106:0.000000
El doble del complemento es:@0.073058:0.887595:0.286482:0.887595:0.286482:0.871882:0.073058:0.871882:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
2 90º:@0.244779:0.915678:0.288165:0.915678:0.288165:0.899965:0.244779:0.899965:0.000000:0.000000:0.000000:0.000000:0.000000
(:@0.254792:0.916260:0.260922:0.916260:0.260922:0.898606:0.254792:0.898606:0.000000
– ):@0.289177:0.916260:0.314009:0.916260:0.314009:0.898606:0.289177:0.898606:0.000000:0.000000:0.000000
x:@0.299393:0.915678:0.306848:0.915678:0.306848:0.899272:0.299393:0.899272:0.000000
De acuerdo con el problema,:@0.514187:0.136895:0.725133:0.136895:0.725133:0.121183:0.514187:0.121183:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.651708:0.164979:0.659163:0.164979:0.659163:0.148572:0.651708:0.148572:0.000000
= (:@0.660194:0.165561:0.692683:0.165561:0.692683:0.147907:0.660194:0.147907:0.000000:0.000000:0.000000
2 90º:@0.676539:0.164979:0.719925:0.164979:0.719925:0.149266:0.676539:0.149266:0.000000:0.000000:0.000000:0.000000:0.000000
– )+:@0.720938:0.165561:0.762115:0.165561:0.762115:0.147907:0.720938:0.147907:0.000000:0.000000:0.000000:0.000000
x:@0.731154:0.164979:0.738609:0.164979:0.738609:0.148572:0.731154:0.148572:0.000000
12º:@0.763127:0.164979:0.789357:0.164979:0.789357:0.149266:0.763127:0.149266:0.000000:0.000000:0.000000
x:@0.653843:0.193062:0.661298:0.193062:0.661298:0.176656:0.653843:0.176656:0.000000
=:@0.662329:0.193644:0.677662:0.193644:0.677662:0.175990:0.662329:0.175990:0.000000
180º 2:@0.678675:0.193062:0.735111:0.193062:0.735111:0.177349:0.678675:0.177349:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.715912:0.193644:0.725116:0.193644:0.725116:0.175990:0.715912:0.175990:0.000000
x:@0.736142:0.193062:0.743597:0.193062:0.743597:0.176656:0.736142:0.176656:0.000000
+:@0.744628:0.193644:0.759961:0.193644:0.759961:0.175990:0.744628:0.175990:0.000000
12º:@0.760973:0.193062:0.787204:0.193062:0.787204:0.177349:0.760973:0.177349:0.000000:0.000000:0.000000
x:@0.675619:0.221145:0.683074:0.221145:0.683074:0.204739:0.675619:0.204739:0.000000
=:@0.684105:0.221727:0.699438:0.221727:0.699438:0.204073:0.684105:0.204073:0.000000
192º 2:@0.700450:0.221145:0.756887:0.221145:0.756887:0.205432:0.700450:0.205432:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.737688:0.221727:0.746892:0.221727:0.746892:0.204073:0.737688:0.204073:0.000000
x:@0.757918:0.221145:0.765373:0.221145:0.765373:0.204739:0.757918:0.204739:0.000000
Sumando 2  a lado y lado, obtenemos::@0.514151:0.249228:0.796302:0.249228:0.796302:0.233515:0.514151:0.233515:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.597867:0.249228:0.605322:0.249228:0.605322:0.232822:0.597867:0.232822:0.000000
x:@0.642946:0.277311:0.650401:0.277311:0.650401:0.260905:0.642946:0.260905:0.000000
+2:@0.651432:0.277311:0.672416:0.277311:0.672416:0.261598:0.651432:0.261598:0.000000:0.000000
x:@0.673429:0.277311:0.680883:0.277311:0.680883:0.260905:0.673429:0.260905:0.000000
=:@0.681914:0.277893:0.697248:0.277893:0.697248:0.260239:0.681914:0.260239:0.000000
192º 2:@0.698260:0.277311:0.754697:0.277311:0.754697:0.261598:0.698260:0.261598:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.735498:0.277893:0.744701:0.277893:0.744701:0.260239:0.735498:0.260239:0.000000
x:@0.755727:0.277311:0.763182:0.277311:0.763182:0.260905:0.755727:0.260905:0.000000
+:@0.764213:0.277893:0.779546:0.277893:0.779546:0.260239:0.764213:0.260239:0.000000
2:@0.780559:0.277311:0.789542:0.277311:0.789542:0.261598:0.780559:0.261598:0.000000
x:@0.790572:0.277311:0.798027:0.277311:0.798027:0.260905:0.790572:0.260905:0.000000
3:@0.684933:0.305394:0.693916:0.305394:0.693916:0.289681:0.684933:0.289681:0.000000
x:@0.694947:0.305394:0.702402:0.305394:0.702402:0.288988:0.694947:0.288988:0.000000
=:@0.703432:0.305977:0.718766:0.305977:0.718766:0.288322:0.703432:0.288322:0.000000
192º:@0.719778:0.305394:0.756022:0.305394:0.756022:0.289681:0.719778:0.289681:0.000000:0.000000:0.000000:0.000000
x:@0.694947:0.333477:0.702402:0.333477:0.702402:0.317071:0.694947:0.317071:0.000000
=:@0.703432:0.334060:0.718766:0.334060:0.718766:0.316405:0.703432:0.316405:0.000000
64º:@0.719778:0.333477:0.746008:0.333477:0.746008:0.317764:0.719778:0.317764:0.000000:0.000000:0.000000
Para comprobar, se halla el complemento de 64º, que es :@0.514132:0.361560:0.930666:0.361560:0.930666:0.345848:0.514132:0.345848:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
26º. El doble de 26º es 52º y 64º es 12º más que 52º; es :@0.514132:0.378202:0.930974:0.378202:0.930974:0.362489:0.514132:0.362489:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
decir, es 12º más que el doble de su complemento.:@0.514132:0.394844:0.883987:0.394844:0.883987:0.379131:0.514132:0.379131:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Ejemplo 3:@0.514132:0.422927:0.590504:0.422927:0.590504:0.406257:0.514132:0.406257:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Halla el valor de  , y teniendo en cuenta la gráfica.:@0.514132:0.451010:0.873703:0.451010:0.873703:0.435297:0.514132:0.435297:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.632491:0.451010:0.639946:0.451010:0.639946:0.434604:0.632491:0.434604:0.000000
Gráfica 2.13 opuestos por el vértice:@0.587816:0.479093:0.853242:0.479093:0.853242:0.462424:0.587816:0.462424:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.628801:0.519442:0.638031:0.519442:0.638031:0.503296:0.628801:0.503296:0.000000
x:@0.639166:0.519442:0.646826:0.519442:0.646826:0.502584:0.639166:0.502584:0.000000
:@0.647961:0.520040:0.663717:0.520040:0.663717:0.501900:0.647961:0.501900:0.000000
10°:@0.664851:0.519442:0.691142:0.519442:0.691142:0.503296:0.664851:0.503296:0.000000:0.000000:0.000000
4:@0.686659:0.574134:0.695889:0.574134:0.695889:0.557988:0.686659:0.557988:0.000000
x:@0.697024:0.574134:0.704684:0.574134:0.704684:0.557276:0.697024:0.557276:0.000000
:@0.705819:0.574732:0.715276:0.574732:0.715276:0.556592:0.705819:0.556592:0.000000
25°:@0.716411:0.574134:0.742702:0.574134:0.742702:0.557988:0.716411:0.557988:0.000000:0.000000:0.000000
A:@0.681382:0.539392:0.692958:0.539392:0.692958:0.522263:0.681382:0.522263:0.000000
B:@0.738125:0.518344:0.748376:0.518344:0.748376:0.501216:0.738125:0.501216:0.000000
C:@0.571321:0.541957:0.582291:0.541957:0.582291:0.524828:0.571321:0.524828:0.000000
D:@0.635667:0.585591:0.648264:0.585591:0.648264:0.568462:0.635667:0.568462:0.000000
E:@0.856432:0.585876:0.865738:0.585876:0.865738:0.568747:0.856432:0.568747:0.000000
:@0.717451:0.540760:0.727968:0.540760:0.727968:0.522620:0.717451:0.522620:0.000000
El :@0.514231:0.628478:0.530632:0.628478:0.530632:0.612765:0.514231:0.612765:0.000000:0.000000:0.000000
∡:@0.531002:0.629060:0.546335:0.629060:0.546335:0.611406:0.531002:0.611406:0.000000
CAB:@0.546280:0.628478:0.574829:0.628478:0.574829:0.612072:0.546280:0.612072:0.000000:0.000000:0.000000
 es opuesto por el vértice con el ángulo :@0.574792:0.628478:0.869130:0.628478:0.869130:0.612765:0.574792:0.612765:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∡:@0.869732:0.629060:0.885065:0.629060:0.885065:0.611406:0.869732:0.611406:0.000000
DAE:@0.885010:0.628478:0.914461:0.628478:0.914461:0.612072:0.885010:0.612072:0.000000:0.000000:0.000000
 y :@0.914425:0.628478:0.930936:0.628478:0.930936:0.612765:0.914425:0.612765:0.000000:0.000000:0.000000
sus medidas son iguales. Luego, 4:@0.514214:0.645119:0.758108:0.645119:0.758108:0.629407:0.514214:0.629407:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
x:@0.758920:0.645119:0.766375:0.645119:0.766375:0.628713:0.758920:0.628713:0.000000
–:@0.767406:0.645702:0.776610:0.645702:0.776610:0.628048:0.767406:0.628048:0.000000
25º 3:@0.777622:0.645119:0.830193:0.645119:0.830193:0.629407:0.777622:0.629407:0.000000:0.000000:0.000000:0.000000:0.000000
∙:@0.804865:0.645702:0.820198:0.645702:0.820198:0.628048:0.804865:0.628048:0.000000
x:@0.831224:0.645119:0.838679:0.645119:0.838679:0.628713:0.831224:0.628713:0.000000
+:@0.839710:0.645702:0.855043:0.645702:0.855043:0.628048:0.839710:0.628048:0.000000
10º:@0.856055:0.645119:0.882286:0.645119:0.882286:0.629407:0.856055:0.629407:0.000000:0.000000:0.000000
Restando 3x y sumando 25º a lado y lado, obtenemos.:@0.514196:0.673203:0.906002:0.673203:0.906002:0.657490:0.514196:0.657490:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
4:@0.581548:0.701286:0.590531:0.701286:0.590531:0.685573:0.581548:0.685573:0.000000
x:@0.591561:0.701286:0.599016:0.701286:0.599016:0.684880:0.591561:0.684880:0.000000
–:@0.600047:0.701868:0.609251:0.701868:0.609251:0.684214:0.600047:0.684214:0.000000
25º 3:@0.610263:0.701286:0.656705:0.701286:0.656705:0.685573:0.610263:0.685573:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.637506:0.701868:0.646710:0.701868:0.646710:0.684214:0.637506:0.684214:0.000000
x:@0.657736:0.701286:0.665190:0.701286:0.665190:0.684880:0.657736:0.684880:0.000000
+:@0.666221:0.701868:0.681555:0.701868:0.681555:0.684214:0.666221:0.684214:0.000000
25º 3:@0.682567:0.701286:0.735138:0.701286:0.735138:0.685573:0.682567:0.685573:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.709810:0.701868:0.725143:0.701868:0.725143:0.684214:0.709810:0.684214:0.000000
x:@0.736169:0.701286:0.743624:0.701286:0.743624:0.684880:0.736169:0.684880:0.000000
+:@0.744655:0.701868:0.759988:0.701868:0.759988:0.684214:0.744655:0.684214:0.000000
10º 3:@0.761000:0.701286:0.807442:0.701286:0.807442:0.685573:0.761000:0.685573:0.000000:0.000000:0.000000:0.000000:0.000000
–:@0.788243:0.701868:0.797447:0.701868:0.797447:0.684214:0.788243:0.684214:0.000000
x:@0.808473:0.701286:0.815927:0.701286:0.815927:0.684880:0.808473:0.684880:0.000000
+:@0.816958:0.701868:0.832292:0.701868:0.832292:0.684214:0.816958:0.684214:0.000000
25º:@0.833304:0.701286:0.859534:0.701286:0.859534:0.685573:0.833304:0.685573:0.000000:0.000000:0.000000
x:@0.695010:0.729369:0.702465:0.729369:0.702465:0.712963:0.695010:0.712963:0.000000
=:@0.703496:0.729951:0.718829:0.729951:0.718829:0.712297:0.703496:0.712297:0.000000
35º:@0.719842:0.729369:0.746072:0.729369:0.746072:0.713656:0.719842:0.713656:0.000000:0.000000:0.000000
Luego, el  CAB es 3 35º:@0.514196:0.757452:0.696059:0.757452:0.696059:0.741739:0.514196:0.741739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∡:@0.583591:0.758034:0.598924:0.758034:0.598924:0.740380:0.583591:0.740380:0.000000
(:@0.662687:0.758034:0.668817:0.758034:0.668817:0.740380:0.662687:0.740380:0.000000
)+:@0.697072:0.758034:0.719547:0.758034:0.719547:0.740380:0.697072:0.740380:0.000000:0.000000
10º 115º:@0.720559:0.757452:0.800392:0.757452:0.800392:0.741739:0.720559:0.741739:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.747802:0.758034:0.763135:0.758034:0.763135:0.740380:0.747802:0.740380:0.000000
El  CAB y el  ABE son adyacentes. Luego, la suma de sus :@0.514196:0.785535:0.931116:0.785535:0.931116:0.769822:0.514196:0.769822:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
∡:@0.529897:0.786117:0.545230:0.786117:0.545230:0.768463:0.529897:0.768463:0.000000
∡:@0.606232:0.786117:0.621565:0.786117:0.621565:0.768463:0.606232:0.768463:0.000000
medidas es 180º.:@0.514196:0.802177:0.636402:0.802177:0.636402:0.786464:0.514196:0.786464:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Es decir que 115º:@0.514196:0.830260:0.642106:0.830260:0.642106:0.814547:0.514196:0.814547:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
+ =:@0.643047:0.830842:0.683230:0.830842:0.683230:0.813188:0.643047:0.813188:0.000000:0.000000:0.000000
y:@0.659392:0.830260:0.666866:0.830260:0.666866:0.813854:0.659392:0.813854:0.000000
180º:@0.684242:0.830260:0.720486:0.830260:0.720486:0.814547:0.684242:0.814547:0.000000:0.000000:0.000000:0.000000
Restando 115º a lado y lado, obtenemos:@0.514196:0.858343:0.806131:0.858343:0.806131:0.842630:0.514196:0.842630:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
115°:@0.626701:0.886426:0.658840:0.886426:0.658840:0.870713:0.626701:0.870713:0.000000:0.000000:0.000000:0.000000
+ –:@0.658730:0.887009:0.692783:0.887009:0.692783:0.869354:0.658730:0.869354:0.000000:0.000000:0.000000
y:@0.675075:0.886426:0.682549:0.886426:0.682549:0.870020:0.675075:0.870020:0.000000
115° 180° 115°:@0.692691:0.886426:0.814344:0.886426:0.814344:0.870713:0.692691:0.870713:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
=:@0.724720:0.887009:0.740053:0.887009:0.740053:0.869354:0.724720:0.869354:0.000000
–:@0.773094:0.887009:0.782297:0.887009:0.782297:0.869354:0.773094:0.869354:0.000000
Luego, :@0.514159:0.914509:0.567047:0.914509:0.567047:0.898796:0.514159:0.898796:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
y:@0.566933:0.914509:0.574406:0.914509:0.574406:0.898103:0.566933:0.898103:0.000000
=:@0.575437:0.915092:0.590770:0.915092:0.590770:0.897437:0.575437:0.897437:0.000000
65º:@0.591782:0.914509:0.618013:0.914509:0.618013:0.898796:0.591782:0.898796:0.000000:0.000000:0.000000
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