84:@0.048054:0.510692:0.066961:0.510692:0.066961:0.494068:0.048054:0.494068:0.000000:0.000000
Tema:@0.047190:0.135475:0.083321:0.135475:0.083321:0.113749:0.047190:0.113749:0.000000:0.000000:0.000000:0.000000
1. :@0.115209:0.589294:0.132107:0.589294:0.132107:0.572159:0.115209:0.572159:0.000000:0.000000:0.000000
Colorea:@0.148452:0.589294:0.207476:0.589294:0.207476:0.572670:0.148452:0.572670:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 con un mismo color las parejas de figuras congruentes.:@0.207476:0.589294:0.614854:0.589294:0.614854:0.572906:0.207476:0.572906:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Taller:@0.176012:0.548056:0.236907:0.548056:0.236907:0.514109:0.176012:0.514109:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
I.M.4.5.1. Construye figuras simétricas; resuelve problemas geométricos que impliquen el cálculo de longitudes con la aplicación de :@0.257033:0.525522:0.877734:0.525522:0.877734:0.515092:0.257033:0.515092:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
conceptos de semejanza y la aplicación del teorema de Tales; justifica procesos aplicando los conceptos de congruencia y semejanza. :@0.257033:0.536083:0.877668:0.536083:0.877668:0.525654:0.257033:0.525654:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
(I.1., I.4.):@0.257033:0.546644:0.292412:0.546644:0.292412:0.536215:0.257033:0.536215:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
En aritmética, el concepto de igualdad tiene que ver con cantidades que tienen el mismo valor. En geo-:@0.115209:0.167757:0.879901:0.167757:0.879901:0.151368:0.115209:0.151368:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
metría el concepto análogo a la igualdad de cantidades se le denomina congruencia. Dos polígonos son :@0.115209:0.184353:0.883844:0.184353:0.883844:0.167964:0.115209:0.167964:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
congruentes si los lados del primer polígono tienen las mismas medidas que los correspondientes lados :@0.115209:0.200949:0.883969:0.200949:0.883969:0.184560:0.115209:0.184560:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
del segundo polígono, y los ángulos internos del primer polígono tienen igual medida que los ángulos :@0.115209:0.217546:0.883899:0.217546:0.883899:0.201157:0.115209:0.201157:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
internos correspondientes del otro polígono.  :@0.115209:0.234142:0.451876:0.234142:0.451876:0.217753:0.115209:0.217753:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
El símbolo de congruencia es  .:@0.115209:0.257861:0.347672:0.257861:0.347672:0.241472:0.115209:0.241472:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≅:@0.334349:0.258539:0.344465:0.258539:0.344465:0.242966:0.334349:0.242966:0.000000
Nota: :@0.115209:0.281580:0.162052:0.281580:0.162052:0.264679:0.115209:0.264679:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
si dos figuras son congruentes, al colocar la una sobre la otra, se las puede acomodar de forma que  :@0.161776:0.281580:0.883936:0.281580:0.883936:0.265191:0.161776:0.265191:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
coincidan perfectamente.:@0.115209:0.298176:0.303886:0.298176:0.303886:0.281788:0.115209:0.281788:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Actividad resuelta:@0.115209:0.330863:0.272331:0.330863:0.272331:0.312425:0.115209:0.312425:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Pintamos:@0.115209:0.350709:0.186948:0.350709:0.186948:0.334085:0.115209:0.334085:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
 los elementos congruentes de las figuras con el mismo color.:@0.186948:0.350709:0.637555:0.350709:0.637555:0.334320:0.186948:0.334320:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Congruencia:@0.115891:0.141978:0.294957:0.141978:0.294957:0.101242:0.115891:0.101242:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
3:@0.054244:0.122645:0.076267:0.122645:0.076267:0.065614:0.054244:0.065614:0.000000
M.4.2.5. Definir e identificar figuras geométricas semejantes, de acuerdo a las medidas de los ángulos y a la relación entre las medidas de los lados, determinando :@0.125388:0.069719:0.877826:0.069719:0.877826:0.059289:0.125388:0.059289:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
el factor de escala entre las figuras (teorema de Thales).:@0.125388:0.080280:0.381224:0.080280:0.381224:0.069851:0.125388:0.069851:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
X:@0.306925:0.372775:0.315991:0.372775:0.315991:0.356413:0.306925:0.356413:0.000000
Z:@0.390218:0.396881:0.399505:0.396881:0.399505:0.380520:0.390218:0.380520:0.000000
Y:@0.309781:0.470099:0.318700:0.470099:0.318700:0.453737:0.309781:0.453737:0.000000
C:@0.142403:0.387407:0.152317:0.387407:0.152317:0.371046:0.142403:0.371046:0.000000
A:@0.116217:0.457098:0.126113:0.457098:0.126113:0.440737:0.116217:0.440737:0.000000
B:@0.240954:0.456185:0.249799:0.456185:0.249799:0.439824:0.240954:0.439824:0.000000
Δ:@0.215117:0.490135:0.226394:0.490135:0.226394:0.474562:0.215117:0.474562:0.000000
ABC    XYZ:@0.226394:0.489457:0.310867:0.489457:0.310867:0.473096:0.226394:0.473096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≅ Δ:@0.258366:0.490135:0.283078:0.490135:0.283078:0.474562:0.258366:0.474562:0.000000:0.000000:0.000000
A:@0.496795:0.386877:0.506690:0.386877:0.506690:0.370515:0.496795:0.370515:0.000000
C:@0.595125:0.387706:0.605039:0.387706:0.605039:0.371345:0.595125:0.371345:0.000000
B:@0.496795:0.455682:0.505640:0.455682:0.505640:0.439321:0.496795:0.439321:0.000000
D:@0.643479:0.454424:0.655015:0.454424:0.655015:0.438063:0.643479:0.438063:0.000000
X:@0.863026:0.386877:0.872092:0.386877:0.872092:0.370515:0.863026:0.370515:0.000000
W:@0.863026:0.455682:0.877897:0.455682:0.877897:0.439321:0.863026:0.439321:0.000000
Z:@0.714259:0.386877:0.723547:0.386877:0.723547:0.370515:0.714259:0.370515:0.000000
Y:@0.758430:0.456000:0.767349:0.456000:0.767349:0.439639:0.758430:0.439639:0.000000
ABCD   XYZW:@0.640339:0.489457:0.740328:0.489457:0.740328:0.473096:0.640339:0.473096:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
≅:@0.683847:0.490135:0.693964:0.490135:0.693964:0.474562:0.683847:0.474562:0.000000
Color 1:@0.330608:0.774846:0.382979:0.774846:0.382979:0.758457:0.330608:0.758457:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Color 1:@0.813578:0.638576:0.865949:0.638576:0.865949:0.622187:0.813578:0.622187:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Color 4:@0.317229:0.893399:0.369601:0.893399:0.369601:0.877010:0.317229:0.877010:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Color 4:@0.801213:0.766188:0.853584:0.766188:0.853584:0.749799:0.801213:0.749799:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Color 2:@0.174728:0.766423:0.227100:0.766423:0.227100:0.750034:0.174728:0.750034:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Color 2:@0.799370:0.862723:0.851741:0.862723:0.851741:0.846335:0.799370:0.846335:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Color 3:@0.162769:0.885350:0.215140:0.885350:0.215140:0.868961:0.162769:0.868961:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000
Color 3:@0.663982:0.654591:0.716353:0.654591:0.716353:0.638202:0.663982:0.638202:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000:0.000000