When constructing a "line by bisection", the vector direction of the reference lines will determine the placement and location of the constructed line.
The following screenshot shows two parallel measured lines with their vectors (arrows) pointing in the same direction. The resulting constructed line is created midway between the two lines, with the same vector as the first line.
Flipping the vector of one of the measured lines, the constructed line will be created perpendicular to the measured parallel lines.
If the two measured lines are not parallel, (yet with vectors pointing in the same direction). The constructed line will be created equidistantly, at half of the overall angle.
Again, flipping the vector of one of the measured lines causes the constructed line to be rotated 90° (minus half of the overall angle).