when constructing a perpendicular bisector, why must the compass opening be greater than 1/2 the length of the segment? explain in one to three sentences.
The compass opening must be greater than 1/2 the length of the segment because it ensures that you can construct arcs on either side of the segment that will intersect. If the compass opening were smaller, the arcs would not intersect and thus a perpendicular bisector could not be accurately constructed.
When constructing a perpendicular bisector, the compass opening must be greater than 1/2 the length of the segment to ensure that both arcs intersect. Without a larger compass opening, the arcs may not intersect, making it impossible to construct a perpendicular bisector.
When constructing a perpendicular bisector, the compass opening must be greater than 1/2 the length of the segment because it ensures that the compass can produce a circle that intersects the segment at two distinct points. This is necessary in order to accurately locate the midpoint of the segment, which is essential in constructing the perpendicular bisector.
