Sehnenviereck SS 12: Unterschied zwischen den Versionen

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--[[Benutzer:Oz44oz|Oz44oz]] 22:55, 17. Jul. 2012 (CEST)
 
--[[Benutzer:Oz44oz|Oz44oz]] 22:55, 17. Jul. 2012 (CEST)
  

Version vom 18. Juli 2012, 15:50 Uhr

Inhaltsverzeichnis

Definitionen

Sehne

Durchmesser

Radius

Erarbeitung des Begriffs Sehnenviereck

Sehnenvierecke.pdf

Sehnenviereck

Sätze

Satzfindung

noch allgemeiner, aber immer noch ziemlich speziell: gleichschenklige Trapeze

Jedes gleichschenklige Trapez ist ein Sehnenviereck.

allgemeines Sehnenviereck

Ausgangslage: \ \overline{ABCD} ist ein gleichschenkliges Trapez.

Arbeitsauftrag: Bewegen Sie den Punkt \ C auf dem Kreis. Beobachten Sie, wie sich der rote und der blaue Winkel verändern. Was vermuten Sie bezüglich der Größe von \ \gamma? Was vermuten Sie hinsichtlich der Größen der gegenüberliegenden Winkel im Sehnenviereck?


Der Satz

Satz 1

Satz 2 : Die Umkehrung vom Satz 1

Kriterium

Beweise

1

--Oz44oz 22:55, 17. Jul. 2012 (CEST)

2

--Oz44oz 23:03, 17. Jul. 2012 (CEST)

Beweis vom Satz 1

Beweis 1 Beweis 2 Beweis 3
Sehnenviereck Beweis 1.png Sehnenviereck Beweis 2.png Sehnenviereck Beweis 3.png
Beweisen Sie |\beta| + |\delta| = 180 Beweisen Sie |\beta| + |\delta| = 180 Beweisen Sie |\beta| + |\delta| = 180

--Oz44oz 19:19, 16. Jul. 2012 (CEST)


Voraussetzung:


Behauptung:

Beweis 1:

Beweis vom Satz 2

Beweis 1 Beweis 2
Sehnenviereck Beweis Umkehrung 1.png Sehnenviereck Beweis Umkehrung 2.png
Beweisen Sie..... Beweisen Sie........

--Oz44oz 19:15, 16. Jul. 2012 (CEST)

Voraussetzung:


Behauptung:


Annahme:

Beweis 1:

Beweisidee

--Oz44oz 22:47, 16. Jul. 2012 (CEST)


--Oz44oz 22:45, 17. Jul. 2012 (CEST)