When constructing a perpendicular bisector, why must the compass opening be greater than 1/2 , the length of the segment?
When constructing a perpendicular bisector, the compass opening must be greater than 1/2 the length of the segment in order to ensure that the arcs of the compass intersect beyond the endpoints of the segment.
The perpendicular bisector is constructed by taking the endpoints of the segment as centers and creating arcs of equal radius on both sides of the segment. These arcs should intersect at two points, which are equidistant from the endpoints of the segment.
If the compass opening is less than 1/2 the length of the segment, the arcs may not intersect beyond the endpoints, and the resulting line may not be perpendicular to the segment. It is important for the arcs to intersect beyond the endpoints to ensure that the line is indeed a perpendicular bisector.
By using a compass opening greater than 1/2 the length of the segment, the arcs will intersect beyond the endpoints, allowing for the construction of an accurate perpendicular bisector.
When constructing a perpendicular bisector, the compass opening must be greater than half the length of the segment because it helps ensure accuracy in the construction.
To construct a perpendicular bisector of a line segment, you need to find the midpoint of the segment and then draw a line perpendicular to it, passing through the midpoint. This creates two equal segments on either side of the perpendicular line.
If the compass opening is smaller than half the length of the segment, there is a risk that the arcs drawn on each side of the midpoint will not intersect, resulting in a line that is not perpendicular to the original segment.
By using a compass opening greater than half the length of the segment, the arcs drawn on either side of the midpoint will intersect, guaranteeing an accurate perpendicular bisector construction.