Sehnenviereck SS 12: Unterschied zwischen den Versionen

Aktuelle Version vom 18. Juli 2012, 21:59 Uhr

Definitionen

Kreissehne

1. Es sei $\ k$ ein Kreis. Eine Sehne des Kreises ist jede Strecke, deren Anfangs- und Endpunkte Element des Kreises $\ k$ sind.

2. ..........

Durchmesser

1. Es sei $\ k$ ein Kreis mit dem Mittelpunkt $\ M$ . Ferner seien $\ A$ und $\ B$ zwei Punkte des Kreises $\ k$ . Ein Durchmesser ist die Strecke $\overline {AB}$ , für die gilt $\operatorname{Zw} \left( A, M, B\right)\wedge A,B\in \ k$ .

Radius

1. Es sei $\ k$ ein Kreis mit dem Mittelpunkt $\ M$ . Jede Strecke, die den Anfangspunkt in $\ M$ und den Endpunkt in einem beliebigen Punkt des Kreises $\ k$ hat, nennt man Radius.

Erarbeitung des Begriffs Sehnenviereck

Sehnenviereck

Ein Viereck, dessen Seiten Sehnen ein und desselben Kreises $k$ sind, heißt Sehnenviereck.

Sätze

Satzfindung

sehr speziell: Quadrate

Jedes Quadrat hat einen Umkreis und ist somit ein Sehnenviereck.

weniger speziell, aber immer noch ziemlich speziell: Rechtecke

Jedes Rechteck ist ein Sehnenviereck.

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 über die gegenüberliegenden Winkel im Sehnenviereck

Satz 1

In jedem Sehnenviereck sind die gegenüberliegenden Winkel supplementär.

--Oz44oz 20:32, 18. Jul. 2012 (CEST)

Satz 2 : Die Umkehrung vom Satz 1

Wenn in einem Viereck die gegenüberliegenden Winkel supplementär sind, dann ist das Viereck ein Sehnenviereck.

Kriterium

Ein Viereck ist .........

Beweise

wir wissen

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

zu zeigen:

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

Beweis vom Satz 1

Beweis 1	Beweis 2	Beweis 3

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

Annahme: $D$ liegt ..	Annahme: $D$ liegt ..

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

Voraussetzung:

Behauptung:

Annahme:

Beweis 1:

Funktionale Betrachtung

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

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

@@ Zeile 1: / Zeile 1: @@
 == Definitionen ==
-=== Sehne ===
+=== Kreissehne ===
+.   Es sei <math>\ k</math> ein Kreis. Eine Sehne des Kreises ist jede Strecke, deren Anfangs- und Endpunkte Element des Kreises <math>\ k</math> sind.
+.   ..........
+=== Durchmesser===
-=== Sehnenviereck ===
+.   Es sei <math>\ k</math> ein Kreis mit dem Mittelpunkt <math>\ M </math>. Ferner seien <math>\ A</math> und <math>\ B </math> zwei Punkte des Kreises <math>\ k</math>. Ein Durchmesser ist die Strecke <math>\overline {AB}</math>, für die gilt <math> \operatorname{Zw} \left( A, M, B\right)\wedge A,B\in \ k</math>.
+=== Radius ===
+.   Es sei <math>\ k</math> ein Kreis mit dem Mittelpunkt <math>\ M </math>. Jede Strecke, die den Anfangspunkt in <math>\ M </math> und den Endpunkt in einem beliebigen Punkt des Kreises <math>\ k</math> hat, nennt man Radius.
+=== Erarbeitung des Begriffs Sehnenviereck ===
+[[Datei:Sehnenvierecke.pdf]]
+=== Sehnenviereck ===
+Ein Viereck, dessen Seiten Sehnen ein und desselben Kreises <math>k</math> sind, heißt Sehnenviereck.
 == Sätze ==
-===Betrachtung===
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showResetIcon = "false" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />--[[Benutzer:Oz44oz|Oz44oz]] 23:10, 13. Jul. 2012 (CEST)
+===Satzfindung===
-===Der Satz ===
+==== sehr speziell: Quadrate ====
+Jedes Quadrat hat einen Umkreis und ist somit ein Sehnenviereck.<br /><br />
+[[Bild:Quadrat_als_Sehnenviereck.png]]
+==== weniger speziell, aber immer noch ziemlich speziell: Rechtecke ====
+Jedes Rechteck ist ein Sehnenviereck.
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+==== noch allgemeiner, aber immer noch ziemlich speziell: gleichschenklige Trapeze ====
+Jedes gleichschenklige Trapez ist ein Sehnenviereck.
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+==== allgemeines Sehnenviereck ====
+Ausgangslage: <math>\ \overline{ABCD}</math> ist ein gleichschenkliges Trapez.
+Arbeitsauftrag: Bewegen Sie den Punkt <math>\ C</math> auf dem Kreis. Beobachten Sie, wie sich der rote und der blaue Winkel verändern. Was vermuten Sie bezüglich der Größe von <math>\ \gamma</math>? Was vermuten Sie hinsichtlich der Größen der gegenüberliegenden Winkel im Sehnenviereck?
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+===Der Satz über die gegenüberliegenden Winkel im Sehnenviereck ===
+====Satz 1 ====
+'''In jedem Sehnenviereck sind die gegenüberliegenden Winkel supplementär.'''
+<ggb_applet width="1008" height="411"  version="4.0" 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" showResetIcon = "false" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />--[[Benutzer:Oz44oz|Oz44oz]] 20:32, 18. Jul. 2012 (CEST)
+====Satz 2 : Die Umkehrung vom Satz 1====
+Wenn in einem Viereck die gegenüberliegenden Winkel supplementär sind, dann ist das Viereck ein Sehnenviereck.
+===Kriterium ===
+Ein Viereck ist .........
 ==Beweise==
+===wir wissen===
+<ggb_applet width="1008" height="421"  version="4.0" 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showResetIcon = "false" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
+--[[Benutzer:Oz44oz|Oz44oz]] 22:55, 17. Jul. 2012 (CEST)
+===zu zeigen:===
+<ggb_applet width="1008" height="421"  version="4.0" 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" showResetIcon = "false" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
+--[[Benutzer:Oz44oz|Oz44oz]] 23:03, 17. Jul. 2012 (CEST)
+===Beweis vom Satz 1===
+{| class="wikitable"
+!Beweis 1!!Beweis 2!!Beweis 3
+|-
+| [[Datei:Sehnenviereck_Beweis_1.png| 300px]] || [[Datei:Sehnenviereck_Beweis_2.png| 300px]] || [[Datei:Sehnenviereck_Beweis_3.png| 300px]]
+|-
+| Beweisen Sie <math>|\beta|</math> + <math>|\delta|</math> = 180°|| Beweisen Sie <math>|\beta|</math> + <math>|\delta|</math> = 180° || Beweisen Sie <math>|\beta|</math> + <math>|\delta|</math> = 180°
+|}
+--[[Benutzer:Oz44oz|Oz44oz]] 19:19, 16. Jul. 2012 (CEST)
+'''Voraussetzung:'''
+'''Behauptung:'''
+'''Beweis 1:'''
+===Beweis vom Satz 2===
+{| class="wikitable"
+!Beweis 1!!Beweis 2
+|-
+| [[Datei:Sehnenviereck_Beweis_Umkehrung_1.png| 300px]] || [[Datei:Sehnenviereck_Beweis_Umkehrung_2.png| 300px]]
+|-
+|Annahme: <math>D</math> liegt .. || Annahme: <math>D</math> liegt ..
+|}
+--[[Benutzer:Oz44oz|Oz44oz]] 19:15, 16. Jul. 2012 (CEST)
+'''Voraussetzung:'''
+'''Behauptung:'''
+'''Annahme:'''
+'''Beweis 1:'''
+===Funktionale Betrachtung===
+<ggb_applet width="1008" height="411"  version="4.0" 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+--[[Benutzer:Oz44oz|Oz44oz]] 22:47, 16. Jul. 2012 (CEST)
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+--[[Benutzer:Oz44oz|Oz44oz]] 22:45, 17. Jul. 2012 (CEST)