1. when constructing a perpendicular bisector why must the compass opening be greater than the length of the segment?

2. when constructing an angle bisector why must the arcs intersect?

1)  as follows are steps how to construct a perpendicular bisector
Place the compass at one end of line segment.
Adjust the compass to slightly longer than half the line segment length.
Draw arcs above and below the line.
Keeping the same compass width, draw arcs from other end of line.
Place ruler where the arcs cross, and draw the line segment.

so the answer should be for precising arcs intersect

2)  for adjusting the line bisector which  divides it into two equal angles