Die Kongruenzsätze SoSe 12: Unterschied zwischen den Versionen

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(Die Seite wurde neu angelegt: „===Die Kongruenzsätze=== Wir haben im Abschnitt über die Kongruenzrelation die Defin…“)
 
(→‎Die Kongruenzsätze)
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Wir haben im Abschnitt über die [[Die Kongruenzrelation, Geradenspiegelung als Kongruenzabbildung SoSe_12|Kongruenzrelation]] die Definition Dreieckskongruenz kennengelernt. Ein Dreieck ist dann kongruent zu einem anderen Dreieck, wenn es in allen seinen "Stücken" (Seiten und Winkel) übereinstimmt, d.h. die Stücke jeweils kongruent zueinander sind. Wir werden jetzt sehen, dass die Kongruenz von zwei Dreiecken bereits sichergestellt sein kann, wenn diese  in drei Stücken übereinstimmen.
 
Wir haben im Abschnitt über die [[Die Kongruenzrelation, Geradenspiegelung als Kongruenzabbildung SoSe_12|Kongruenzrelation]] die Definition Dreieckskongruenz kennengelernt. Ein Dreieck ist dann kongruent zu einem anderen Dreieck, wenn es in allen seinen "Stücken" (Seiten und Winkel) übereinstimmt, d.h. die Stücke jeweils kongruent zueinander sind. Wir werden jetzt sehen, dass die Kongruenz von zwei Dreiecken bereits sichergestellt sein kann, wenn diese  in drei Stücken übereinstimmen.
  
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=====Satz XII.1 (Kongruenzsatz sss):
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=====Satz XII.1 (Kongruenzsatz sss):=====
 
Zwei Dreiecke <math>\overline{ABC}</math> und <math>\overline{DEF}</math> sind kongruent zueinander, wenn gilt: <math>\left| AB \right| =\left| DE \right|,\;\left| BC \right|=\left| EF \right|,\;und\;\left| AC \right|=\left| DF \right|    </math>.<br />
 
Zwei Dreiecke <math>\overline{ABC}</math> und <math>\overline{DEF}</math> sind kongruent zueinander, wenn gilt: <math>\left| AB \right| =\left| DE \right|,\;\left| BC \right|=\left| EF \right|,\;und\;\left| AC \right|=\left| DF \right|    </math>.<br />
 
'''Beweis:'''<br /><br />  
 
'''Beweis:'''<br /><br />  
 
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Version vom 1. Juli 2012, 20:38 Uhr

Die Kongruenzsätze

Wir haben im Abschnitt über die Kongruenzrelation die Definition Dreieckskongruenz kennengelernt. Ein Dreieck ist dann kongruent zu einem anderen Dreieck, wenn es in allen seinen "Stücken" (Seiten und Winkel) übereinstimmt, d.h. die Stücke jeweils kongruent zueinander sind. Wir werden jetzt sehen, dass die Kongruenz von zwei Dreiecken bereits sichergestellt sein kann, wenn diese in drei Stücken übereinstimmen.

Satz XII.1 (Kongruenzsatz sss):

Zwei Dreiecke \overline{ABC} und \overline{DEF} sind kongruent zueinander, wenn gilt: \left| AB \right| =\left| DE \right|,\;\left| BC \right|=\left| EF \right|,\;und\;\left| AC \right|=\left| DF \right| .
Beweis:

Von „http://geometrie.zum.de/index.php?title=Die_Kongruenzsätze_SoSe_12&oldid=15836“