Question

1: When constructing a perpendicular bisector, why must the compass opening be greater than 1/2 the length of the segment?2. When constructing an angle bisector, why must the arcs intersect?

Answer 1

1) A perpendicular bisector to a segment is a perpendicular line that divides the segment into halves. If the compass opening is equal to or less than 1/2 the length of the segment, the two circumferences we are drawing will be tangential or won't overlap at all. In a diagram,

Whereas, what we are trying to achieve is