Satz des Thales: Unterschied zwischen den Versionen

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(Variante)
(Umkehrung Satz des Thales)
 
(26 dazwischenliegende Versionen von 9 Benutzern werden nicht angezeigt)
Zeile 2: Zeile 2:
 
Hier geben Ihnen die Didaktikspezialisten Tipps zum Satz des Thales
 
Hier geben Ihnen die Didaktikspezialisten Tipps zum Satz des Thales
  
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=Satzfindung=
  
==Funktionale Betrachtung==
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==Induktive Satzfindung==
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==Beweisführung==
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==Funktionale Betrachtung==
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+
  
===Variante===
 
<ggb_applet width="884" height="620"  version="3.2" ggbBase64="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" framePossible = "false" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" />
 
--[[Benutzer:&quot;chris&quot;07|&quot;chris&quot;07]] 22:10, 14. Jul. 2010 (UTC)
 
  
===Vielleicht so besser...===
+
===Variante 1===
 +
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<ggb_applet width="1080" height="620"  version="3.2" ggbBase64="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" framePossible = "false" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" />--[[Benutzer:&quot;chris&quot;07|&quot;chris&quot;07]] 17:07, 15. Jul. 2010 (UTC)
 
  
=induktive Satzfindung=
+
===Variante 2===
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+
 
+
=Sehnen verschieben=
+
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+
--[[Benutzer:Mirasol|Mirasol]] 13:52, 9. Jul. 2010 (UTC)
+
Bewege den Punkt A, um die Sehne zu verschieben!
+
 
+
 
+
=Variante a=
+
  
 
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<ggb_applet width="884" height="510"  version="3.2" ggbBase64="UEsDBBQACAAIAIi17jwAAAAAAAAAAAAAAAAMAAAAZ2VvZ2VicmEueG1s3VnLcts2FF03X4FRZzrtTEyDb7KR4pHtpJNp0mTiNJnppgORVxJqilRA0Jb8M930B7rJqjvv+029AEi9rVh+tHHlBc2L173nnHsBSO2DySgjZyBKXuSdlm3RFoE8KVKeDzqtSvb3otbB00ftARQD6AlG+oUYMdlpuZbTUvaKP330VbscFueEZbrLew7nnVafZSW0SDkWwNJyCCCX7Kya8IwzMX3d+w0SWc4bzCQv8nGFq0hRoS0ZpS952bzuqwX7RS4JKfkFoNOOsrX3tS9tqJKMp5zlaj3tG3Yi5JyncthpRZHXIkPggyFO59PIzJYUhUhPpqWEEZn8AqLotGINxdS8OLGn3sqEZaCG6abFNz0LnJ2AlAhcSdgE5iENBE+XXl6Uh0U2N40LnssjNpaV0Ki7telETtUCuJZQ/nbzQQa1zUFQhpCc9orJicHANVO/m471EO1Qb3BUZIUgAgf4Pnaonz3z1H2Up7NeVPehukc9h5p01m7Hju6hnz3z1L0ynhvX6sjtJmqbNsvwkiiDghHFMgs+Yz3IOq0WqXIuXzYvkiendai2GfBTNeqhShc1MJvTvqs52/sr6mmfgsghMxrJkduqqEpyxrJmLe1ICgkf4atpaCJWdP2MDhhrCgMBjeNG4wawxTFGhyvm9n7jhPKhRF8TicmK8UgVywmTF32ep1U+IM+r/FS1oTDJIUjBkqFUdqYSTg4LoXBImcRhKnkhgxFgHkktGq25GXivWrO8LnSKNslYt89pwOaNAtJSY9l4yNDS5EjGpiCWYtbzvSpSWEEPEdVhYlKO1QSKszFAWhcpWQudjHFKnTYLhGgcSzJRfcMIcxW9sShq9sKM1p1MjqnioBd2awEYTD6DzuGv9jo+y+pbcOdeEOrzCaTGMudiHrhv0Vngu8WdFKMRy1OSsxHGfcRFkoEOlquaTBhV4iDMNiiYACvZNCXG1t6vp1kDEjXMkxlKSQ3kvIDIIeZpDmWpq5xcrGdXq/EaYNObQ30t53BPgfwMXStESciE1jqdUrMguWgsE0Ruz2whdm26sBf4Qd0LPiHdpn+36dV1cKBrBZ7tx/MPSqjr1mt0PexhJN/18V8teuPdx9xEUJoKiKmU8D4SsZX8N1r0y9wnG0jvbqd8OXe6N6ostmM2MP38UqoLYu1FNI5o5IaeHYSxH+ucsy3fdgM38JEpJ6ZBvGPpuRkLx7uwcHzD+vVF8qAkTxc/jqYB6XHQHuCf71OPRkFwGx5eYhnYXAiP17hgnyuDqqbMsGY3roI77zm3KINzvF3Lpau46q3GcajnBdSLHZ+6tvtszzaI7/lWhBlCwygMwzh0Qn+XyrpSu/honPGEy+1sveJCFGKFr67hi23InsNdsufwv69hS1u9t1iEws01KLyN9k9goOyb4TxcPwVsB7OsZ5udAu7iDLAZ8+bic4fq3/MsD0UfOwi6j2ngBEbnCHpg+Y4dB8iCF7muH7tG/TGq347C2PWQjoi64R2pX2OeqcL4Ipd4kwF9M1i/oJwCjNXN8HX+TrC8VHf45ZPj1cTPJt6wAV2ZS89M0/NdUurZDTekwNP8qkfPPG7P8H3tJ9vif/5lxR/Gix9zlfAt11kK/9841RztIqKjW9xaberctkZ85k7mWFiKaeh7kedj6QipX8Pq2JEfubhj2qEb3wrVt2y6gumRycXuGrDpdmAFztTAlj6w00mIJxBVan3H86LYNsnrWTR0qR+4eEixfTeo90PbCnyHRrYfunaImR48nNp8JdnrGzJcn2x40GRTrz6K6hff9Z3IjhynPoY6juXixmwHse/iecnzo4fDtv7+d4Xv1PANa3z//ed2wvW3kzOysLcaj45UNc54sVWHmJDGTuDZjtMAddPSus64d03G175hXmDIW2GIiWReKYPGmGXF+VvoZzDREK5wcsMz79Ea5L3dzry9+zvz3nmS7W0uqZsr6t5DLqmbOb+yrLLdOGcPiPP/c2GFyVigJ+qLpxrUdzCRKGps6LS++VgV8sno8tMgs0i36g+wS15KyLIqH3z/zdc2ffIePUmGHHpAUg7kBLgEkjwmPE9hRNKKpJCTN+rXGNIlrOoTZf5RAC9JD85hUEpLz/MBB5+BGF7+kUlS8mRIUlyMY3dBBuLyrxzIB56fQnZgurM8J0MmCTardX8Ql58ufwcS0wOiO3x7XAmc5ByyZDjzYFSV5aKbZADY+BiXGnG5vhQBnpO3kAwR7sbES3nwncFFY7ksc4ngtZaR3C7h+z0clJIJqa8XpP6S1vWWbnN+c5uL3KVbjrd48l7Uy/7iD2/6p+b65/Cn/wBQSwcIfLrPecUGAABAHwAAUEsBAhQAFAAIAAgAiLXuPHy6z3nFBgAAQB8AAAwAAAAAAAAAAAAAAAAAAAAAAGdlb2dlYnJhLnhtbFBLBQYAAAAAAQABADoAAAD/BgAAAAA=" framePossible = "false" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" />
 
--[[Benutzer:&quot;chris&quot;07|&quot;chris&quot;07]] 21:12, 14. Jul. 2010 (UTC)
 
--[[Benutzer:&quot;chris&quot;07|&quot;chris&quot;07]] 21:12, 14. Jul. 2010 (UTC)
==Variante b==
+
 
 +
 
 +
===Variante 3===
 
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--[[Benutzer:&quot;chris&quot;07|&quot;chris&quot;07]] 21:12, 14. Jul. 2010 (UTC)
 
--[[Benutzer:&quot;chris&quot;07|&quot;chris&quot;07]] 21:12, 14. Jul. 2010 (UTC)
  
=induktive Satzfindung einer Umkehrung=
+
=Beweisfindung=
  
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(vgl. Idee von Frau "komplizierter Doppelname" in einer alten Klausur)<br />
+
==ikonisches/halbikonisches Beweisen==
Kann bitte jemand den Satz auf richtige Formulierung kontrollieren?! <br />
+
 
Welche speziellen Art der Einführung von Sätzen im induktiven Bereich lässt sich dieses Beispiel zuordnen?
+
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framePossible = "false" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" />--[[Benutzer:&quot;chris&quot;07|&quot;chris&quot;07]] 17:07, 15. Jul. 2010 (UTC)
=Funktional=
+
 
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+
==Beweisen am Beispiel==
 
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 +
 +
=induktive Satzfindung der allgemeinen Umkehrung=
 +
 +
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 +
 +
Nimmt man statt eines Rechtecks ein Parallelogramm, so lässt sich die Umkehrung des Periphriewinkelsatzes finden:<br />
 +
Die Scheitel kongruente Winkel, deren Schenkel die Eckpunkte einer Strecke AB enthalten, liegen auf einem Kreis, der AB als Sehne hat.--[[Benutzer:Tja???|Tja???]] 09:39, 23. Jul. 2010 (UTC)
 +
 +
=Beweisführung=
 +
 +
==Satz des Thales==
 +
===Satz des Thales===
 +
Es sei k ein Kreis mit einem Durchmesser <math> \overline {AB} </math>. Jeder Peripheriewinkel von k über <math> \overline {AB} </math> ist ein rechter Winkel.--[[Benutzer:Löwenzahn|Löwenzahn]] 15:07, 23. Jul. 2010 (UTC)
 +
 +
Ein Versuch den Satz des Thales  mit dem EP zu beweisen:
 +
 +
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 +
 +
Vor: Dreieck ABC, A,B und C element von k, Kreis K<br />
 +
Beh: y= 90<br />
 +
 +
1) Konstruieren eine Parallele zu AB durch C  (Nach dem EP)<br />
 +
2)Der Winkel < ACE ist Kongruent zu alpha  (Wechselwinkelsatz)<br />
 +
3)Delta ist kongruent zu Betha  (Wechselwinkelsatz)<br />
 +
4)Winkel < ACM ist Kongruent zu alpha  (Basiswinkelsatz)<br />
 +
5) Winkel < MCB ist kongruent zu Betha  (Basiswinkelsatz)<br />
 +
6) <ACE+<ACM+<MCB+<BCD= 180<br />
 +
7)alpha+alpha+betha+Betha= 180  (einsetzten der Kongruenzen)<br />
 +
8) 2*(alpha+betha)= 180    (rechenen in R)<br />
 +
9) alpha+betha=90            (rechenen in R)<br />
 +
10) Y=90<br />
 +
q.e.d<br />
 +
 +
==Umkehrung 1: Satz des Thales==
 +
===Umkehrung Satz des Thales===
 +
Ist <math> \overline {ABC} </math> ein Dreieck mit einem rechten WInkel bei <math> C </math>, so liegt der Punkt <math> C </math> auf dem Thaleskreis, wobei <math> \overline {AB} </math> einen Durchmesser des Kreises <math> k </math>bildet.--[[Benutzer:Löwenzahn|Löwenzahn]] 15:07, 23. Jul. 2010 (UTC)<br />
 +
Anmerkung--[[Benutzer:TimoRR|TimoRR]] 16:13, 26. Jul. 2010 (UTC): Du meinst <math>\overline{AB}</math> ist Durchmesser des Kreises <math>k</math>. !?? Jupp, Danke!--[[Benutzer:Löwenzahn|Löwenzahn]] 16:25, 26. Jul. 2010 (UTC)
 +
 +
==Umkehrung 2: Satz des Thales==
 +
===Umkehrung Satz des Thales===
 +
 +
<br />Ist ein Peripheriewinkel <math>\gamma </math> über einer Sehne <math> s </math> eines Kreises <math> k </math> ein rechter Winkel, so ist die Sehne s ein Durchmesser des Kreises <math> k </math>.--[[Benutzer:Löwenzahn|Löwenzahn]] 15:07, 23. Jul. 2010 (UTC)
 +
 +
<br />Ein [[Beweise_von_Studenten#Umkehrung_des_Satz_des_Thales | Versuch eines Beweises]] besser: zwei Beweis-Ideen, eine über Winkelkonstruktion, die andere via Zentri-Peripheriewinkelsatz...
 +
<br />--[[Benutzer:Heinzvaneugen|Heinzvaneugen]] 10:29, 26. Jul. 2010 (UTC)
 +
 +
===Kommentar zu den Umkehrungen des Thalesstzes--[[Benutzer:*m.g.*|*m.g.*]] 20:43, 23. Jul. 2010 (UTC)===
 +
Es sei <math>\ \alpha</math> ein Winkel und <math>\ k</math> ein Kreis.
 +
Der Satz des Thales hat zwei Voraussetzungen:
 +
 +
# <math>\ \alpha</math> ist Peripheriewinkel von <math>\ k</math>
 +
# über einem Durchmesser von <math> \ k</math>.
 +
 +
Die Behauptung des Thalessatzes: <math>\ \alpha</math> ist ein rechter Winkel.
 +
 +
Aus Gründen der Übersicht benenne ich die Voraussetzungen V1 und V2. Für die Behauptung schreibe ich B.
 +
 +
Satz des Thales:
 +
 +
Aus V1 und V2 folgt B.
 +
 +
Die eigentliche Umkehrung:
 +
 +
Aus B folgt V1 und V2.
 +
 +
Gemischte Umkehrung 1:
 +
 +
Aus B und V1 folgt V2.
 +
 +
Gemischte Umkehrung 2:
 +
 +
Aus B und V2 folgt V1.
 +
 +
<br /><br />Also fehlt uns noch die
 +
 +
==== Eigentliche Umkehrung des Satz von Thales ====
 +
Mein Vorschlag: <br />Es sei ein Dreieck <math> \overline {ABC} </math> mit den schulüblichen Bezeichnungen. Ist <math>\ \gamma</math> ein rechter Winkel, so ist <math> \ c</math>  identisch mit einem Durchmesser des Umkreises des Dreiecks.
 +
<br />--[[Benutzer:Barbarossa|Barbarossa]] 08:38, 25. Jul. 2010 (UTC)

Aktuelle Version vom 26. Juli 2010, 17:25 Uhr

Inhaltsverzeichnis

Ein wenig Didaktik

Hier geben Ihnen die Didaktikspezialisten Tipps zum Satz des Thales

Satzfindung

Induktive Satzfindung

--Gubbel 12:10, 21. Jul. 2010 (UTC)

Funktionale Betrachtung

Variante 1

--"chris"07 21:47, 15. Jul. 2010 (UTC)


Variante 2

--"chris"07 21:12, 14. Jul. 2010 (UTC)


Variante 3

--"chris"07 21:12, 14. Jul. 2010 (UTC)

Beweisfindung

ikonisches/halbikonisches Beweisen

--"chris"07 17:07, 15. Jul. 2010 (UTC)

Beweisen am Beispiel

induktive Satzfindung der allgemeinen Umkehrung

Nimmt man statt eines Rechtecks ein Parallelogramm, so lässt sich die Umkehrung des Periphriewinkelsatzes finden:
Die Scheitel kongruente Winkel, deren Schenkel die Eckpunkte einer Strecke AB enthalten, liegen auf einem Kreis, der AB als Sehne hat.--Tja??? 09:39, 23. Jul. 2010 (UTC)

Beweisführung

Satz des Thales

Satz des Thales

Es sei k ein Kreis mit einem Durchmesser  \overline {AB} . Jeder Peripheriewinkel von k über  \overline {AB} ist ein rechter Winkel.--Löwenzahn 15:07, 23. Jul. 2010 (UTC)

Ein Versuch den Satz des Thales mit dem EP zu beweisen:

Vor: Dreieck ABC, A,B und C element von k, Kreis K
Beh: y= 90

1) Konstruieren eine Parallele zu AB durch C (Nach dem EP)
2)Der Winkel < ACE ist Kongruent zu alpha (Wechselwinkelsatz)
3)Delta ist kongruent zu Betha (Wechselwinkelsatz)
4)Winkel < ACM ist Kongruent zu alpha (Basiswinkelsatz)
5) Winkel < MCB ist kongruent zu Betha (Basiswinkelsatz)
6) <ACE+<ACM+<MCB+<BCD= 180
7)alpha+alpha+betha+Betha= 180 (einsetzten der Kongruenzen)
8) 2*(alpha+betha)= 180 (rechenen in R)
9) alpha+betha=90 (rechenen in R)
10) Y=90
q.e.d

Umkehrung 1: Satz des Thales

Umkehrung Satz des Thales

Ist  \overline {ABC} ein Dreieck mit einem rechten WInkel bei  C , so liegt der Punkt  C auf dem Thaleskreis, wobei  \overline {AB} einen Durchmesser des Kreises  k bildet.--Löwenzahn 15:07, 23. Jul. 2010 (UTC)
Anmerkung--TimoRR 16:13, 26. Jul. 2010 (UTC): Du meinst \overline{AB} ist Durchmesser des Kreises k. !?? Jupp, Danke!--Löwenzahn 16:25, 26. Jul. 2010 (UTC)

Umkehrung 2: Satz des Thales

Umkehrung Satz des Thales


Ist ein Peripheriewinkel \gamma über einer Sehne  s eines Kreises  k ein rechter Winkel, so ist die Sehne s ein Durchmesser des Kreises  k .--Löwenzahn 15:07, 23. Jul. 2010 (UTC)


Ein Versuch eines Beweises besser: zwei Beweis-Ideen, eine über Winkelkonstruktion, die andere via Zentri-Peripheriewinkelsatz...
--Heinzvaneugen 10:29, 26. Jul. 2010 (UTC)

Kommentar zu den Umkehrungen des Thalesstzes--*m.g.* 20:43, 23. Jul. 2010 (UTC)

Es sei \ \alpha ein Winkel und \ k ein Kreis. Der Satz des Thales hat zwei Voraussetzungen:

  1. \ \alpha ist Peripheriewinkel von \ k
  2. über einem Durchmesser von  \ k.

Die Behauptung des Thalessatzes: \ \alpha ist ein rechter Winkel.

Aus Gründen der Übersicht benenne ich die Voraussetzungen V1 und V2. Für die Behauptung schreibe ich B.

Satz des Thales:

Aus V1 und V2 folgt B.

Die eigentliche Umkehrung:

Aus B folgt V1 und V2.

Gemischte Umkehrung 1:

Aus B und V1 folgt V2.

Gemischte Umkehrung 2:

Aus B und V2 folgt V1.



Also fehlt uns noch die

Eigentliche Umkehrung des Satz von Thales

Mein Vorschlag:
Es sei ein Dreieck  \overline {ABC} mit den schulüblichen Bezeichnungen. Ist \ \gamma ein rechter Winkel, so ist  \ c identisch mit einem Durchmesser des Umkreises des Dreiecks.
--Barbarossa 08:38, 25. Jul. 2010 (UTC)