Forum Geometricorum, 1 (2001) 151 -- 160.
Abstract: It is well known that perpendicularity yields an involution on the line at infinity L^\infty mapping perpendicular directions to each other. Many notions of triangle geometry depend on this involution. Since in projective geometry the perpendicular involution is not different from other involutions, theorems using standard perpendicularity in fact are valid more generally.
In this paper we will classify alternative perpendicularities by replacing the orthocenter H by a point P and the line at infinity by a line \ell. We show what coordinates undergo with these changes and give some applications.
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