Source : Webster's Revised Unabridged Dictionary (1913)

Perpendicularity \Per`pen*dic`u*lar"i*ty\, n. [Cf. F.
   perpendicularit['e].]
   The quality or state of being perpendicular.

Source : WordNet®

perpendicularity
     n 1: the relation of opposition between things at right angles
          [syn: {orthogonality}, {orthogonal opposition}]
     2: the quality of being at right angles to a given line or
        plane (especially the plane of the horizon)