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No. All segments have only one perpendicular bisector.
A single line cannot be perpendicular or parallel. These are attributes of two (or more) lines.
A diagonal is a straight line connecting two non-consecutive points in a four or more sided polygon without overlapping any of the sides.
It is a diagonal: nothing else!
According to Wikipedia: A diagonal can refer to a line joining two nonconsecutive vertices of a polygon or polyhedron... See the related link for more detail.