Mittelsenkrechten

Bei den auffälligen Geraden in den letzten beiden Abschnitten handelt es sich jeweils um die [b]Mittelsenkrechte[/b] der zwei Punkte bzw. einer Strecke. Diese kannst du nun in dieser Zeichnung selbst konstruieren.
[list=1][*] Wähle das Werkzeug "Mittelpunkt" [icon]/images/ggb/toolbar/mode_midpoint.png[/icon]und klicke die Punkte A und B an: Der Mittelpunkt der Strecke AB wird angezeigt.[/*][*] Wähle das Werkzeug "Senkrechte" [icon]/images/ggb/toolbar/mode_orthogonal.png[/icon], klicke die Strecke AB und dann den Mittelpunkt an. Es erscheint die gesuchte Mittelsenkrechte.[br][/*][*] Verschiebe mit dem Werkzeug "Bewegen" [icon]/images/ggb/toolbar/mode_move.png[/icon] die Punkte A, B und C.[br] Tipp: Mit dem Werkzeug [icon]https://www.geogebra.org/images/ggb/toolbar/mode_linebisector.png[/icon] kannst du die Mittelsenkrechte auch in einem Schritt konstruieren ([url=http://www.herr-esseling.de/geometrie7/Hilfe_Werkzeuge.html#Mittelsenkrechte]Hilfe[/url])! [br][br][/*][/list]
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[/img]Welche Eigenschaft haben also [i]alle[/i] Punkte, die auf der Mittelsenkrechten der Strecke AB liegen?[br] Versuche, diese Eigenschaft mit Hilfe der Dreiecke ADC und  BDC zu begründen!
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Information: Mittelsenkrechten