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perpendicularity in Euclidean plane

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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 
                         $$l \bot m.$$

\bibitem{Grundlagen}{\sc D. Hilbert}: {\em Grundlagen der Geometrie}. Neunte Auflage, revidiert und erg\"anzt von Paul Bernays.\;  B. G. Teubner Verlagsgesellschaft, Stuttgart (1962).