Die Höhen eines Dreiecks: Unterschied zwischen den Versionen

Aus Geometrie-Wiki
Wechseln zu: Navigation, Suche
(→‎Definition : (Hohe eines Dreiecks auf einer Seite des Dreiecks))
(→‎Definition : (Höhe eines Dreiecks auf einer Seite des Dreiecks))
Zeile 8: Zeile 8:
  
 
<ggb_applet width="660" height="502"  version="3.2" ggbBase64="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" framePossible = "false" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "true" showAlgebraInput = "false" allowRescaling = "true" />
 
<ggb_applet width="660" height="502"  version="3.2" ggbBase64="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" framePossible = "false" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "true" showAlgebraInput = "false" allowRescaling = "true" />
 +
 +
 +
<ggb_applet width="755" height="502"  version="3.2" ggbBase64="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" framePossible = "false" showResetIcon = "true" showAnimationButton = "true" enableRightClick = "true" errorDialogsActive = "true" enableLabelDrags = "true" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "true" showAlgebraInput = "false" allowRescaling = "true" />

Version vom 16. Juli 2010, 07:37 Uhr

Begriff der Höhe eines Dreiecks

Definition : (Höhe eines Dreiecks auf einer Seite des Dreiecks)
Es sei \overline{ABC} ein Dreieck.
Unter der Höhe des Dreiecks \overline{ABC} auf der Seite \overline{AB} versteht man das Lot von \ C auf die Gerade \ AB.
Unter der Höhe des Dreiecks \overline{ABC} auf der Seite \overline{BC} versteht man das Lot von \ A auf die Gerade \ BC.
Unter der Höhe des Dreiecks \overline{ABC} auf der Seite \overline{AC} versteht man das Lot von \ B auf die Gerade \ AC.



Von „http://geometrie.zum.de/index.php?title=Die_Höhen_eines_Dreiecks&oldid=3237“