Question

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

Answer 1

otherwise when you put your compass on other point of line it will never cut the first arc:)

Answer 2

It doesn't actually have to open quite that much, but it does have to be greater than HALF of the segment. Otherwise, when you draw an arc from each end point, the arcs will be too short and won't intersect. If you go with the problem statement, that will be suffice but it is not necessary to be THAT big.

Answer 3

:)