Answer:
C. Use a compass to swing an arc on either side of the segment for each endpoint
Explanation:
- You are given a segment with two endpoints.
- Place the compass on one of the endpoints, and open the compass to a distance more than halfway across the segment.
- Swing an arc on either side of the segment.
- Keeping the compass at the same width, place the compass on the other endpoint and swing arcs on either side so that they intersect the first two arcs created.
- Mark the intersection points of the arcs, and draw a line through those two points.
- The point where this new line crosses the given segment is the midpoint and divides the segment in half.
- When you bisect a segment, you also construct a perpendicular bisector.
Answer A is incorrect. According to step 2, the compass width must be longer than the radius. If it is shorter, the arcs will not cross and therefore not make a point.
Answer B was not provided.
Answer D is incorrect. Congruency only is necessary when copying a line segment. The length of the perpendicular line segment does not apply here.