Question

If a line is the perpendicular bisector of a segment, then it intersects at the midpoint. Is the converse true? Explain.

A. Yes, because perpendicular bisectors always pass through the midpoint
B. Yes, because segments are always divided into equal parts by perpendicular bisectors
C. No, because a line can pass through the midpoint without being a perpendicular bisector
D. No, because perpendicular bisectors do not necessarily intersect at the midpoint

Answer 1

No, a line can pass through the midpoint of a segment without being the perpendicular bisector, as it also needs to form a 90-degree angle with the segment.

Step-by-step explanation:

If a line is the perpendicular bisector of a segment, it does intersect the segment at its midpoint. The converse of this statement would be: If a line intersects a segment at its midpoint, then it is the perpendicular bisector of that segment. The correct answer to this is C. No, because a line can pass through the midpoint of a segment without being a perpendicular bisector. For a line to be a perpendicular bisector, it must not only pass through the midpoint of a segment but also form right angles (90 degrees) with the segment at the point of intersection. Thus, while all perpendicular bisectors intersect segments at their midpoints, not all lines that intersect at the midpoint are perpendicular bisectors.