Parallelogramm aus Seitenmitten des Vierecks: Unterschied zwischen den Versionen

Aus Geometrie-Wiki
Wechseln zu: Navigation, Suche
(Die Seite wurde neu angelegt: „<ggb_applet width="968" height="746" version="4.0" ggbBase64="UEsDBBQACAgIAG5ScEEAAAAAAAAAAAAAAAAWAAAAZ2VvZ2VicmFfamF2YXNjcmlwdC5qc0srzUsuyczPU0hPT/LP88zLLNHQVKi…“)
 
Zeile 1: Zeile 1:
 
<ggb_applet width="968" height="746"  version="4.0" ggbBase64="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" framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
 
<ggb_applet width="968" height="746"  version="4.0" ggbBase64="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" framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" useBrowserForJS = "true" allowRescaling = "true" />
 +
<br />Das ist ja spannend. Das heißt, mit Ausnahme der überschlagenen Vierecke, bei denen alle Seitenmittelpunkte kollinear sind, ergibt sich immer ein Parallelogramm. Tolle Applikation!--[[Benutzer:Tutorin Anne|Tutorin Anne]] 14:33, 16. Nov. 2012 (CET)

Version vom 16. November 2012, 15:33 Uhr


Das ist ja spannend. Das heißt, mit Ausnahme der überschlagenen Vierecke, bei denen alle Seitenmittelpunkte kollinear sind, ergibt sich immer ein Parallelogramm. Tolle Applikation!--Tutorin Anne 14:33, 16. Nov. 2012 (CET)