perpendicularity in Euclidean planePerpendicularityInEuclideanPlane2007-08-28 05:52:082007-09-02 15:23:05DefinitionEuclidean geometry of planeperpendicularityperpendicularorthogonalityorthogonal% this is the default PlanetMath preamble. as your knowledge
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Two lines in the Euclidean plane are {\em perpendicular} to each other if and only if they intersect and two of the angles they form are congruent.
This definition \PMlinkescapetext{bases} on the one in Hilbert's {\em Grundlagen der Geometrie} (``Ein Winkel, welcher einem seiner Nebenwinkel kongruent ist, hei\ss t ein {\em rechter Winkel}'').
The {\em perpendicularity} of $l$ and $m$ is denoted
$$l \perp m.$$
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\bibitem{Grundlagen}{\sc D. Hilbert}: {\em Grundlagen der Geometrie}. Neunte Auflage, revidiert und erg\"anzt von Paul Bernays.\; B. G. Teubner Verlagsgesellschaft, Stuttgart (1962).
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