In der ebenen Geometrie ist die Winkelhalbierende (auch Winkelsymmetrale genannt) eines Winkels die Halbgerade, die durch den Scheitelpunkt des Winkels läuft und das Winkelfeld in zwei deckungsgleiche Teile teilt. In der synthetischen Geometrie werden die Winkelhalbierenden eines schneidenden Geradenpaars ebenfalls durch ihre Eigenschaft als Symmetrieachsen definiert. Die Existenz dieser Winkelhalbierenden ist dort eines der Axiome, die eine frei bewegliche präeuklidische Ebene kennzeichnen. 1 Winkelhalbierende in der ebenen Geometrie 1.1 Konstruktion 1.2 Winkelhalbierendensatz 1.3 Winkelhalbierende im Dreieck 1.4 Winkelhalbierende im Viereck. Konstruktion. Bei dieser Konstruktion wird benutzt, dass die Winkelhalbierende zugleich Mittelsenkrechte in dem gleichschenkligen Dreieck ist, das durch den Scheitel und die zwei ersten Hilfspunkte gegeben ist.
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