Question

When constructing a perpendicular bisector, why must the compass opening be greater than one half the length of the segment?

Answer 1

if the distance is less than 1/2, the 2 circles don't intersect

Answer 2

because if the compass length is less than half the length of the segment the two arcs of the compass will never intersect

Answer 3

Try it for yourself and see.

Answer 4

the compass length does not NEED to be greater than one half the length of a segment. but by having it so, it takes less time to do it.