Question

1. a sheet of paper with points a and b is folded so that a and b match up with each other. explain why the crease in the sheet of paper is the perpendicular bisector of segment ab. (assume the conjecture that the set of points equidistant from a and b is the perpendicular bisector of segment ab is true.)

Explanation:

When the paper is folded so that A and B match, any point on the crease is equidistant from A and B. By the given conjecture, the set of points equidistant from A and B is the perpendicular bisector of segment AB. So the crease is the perpendicular bisector of AB.

Answer:

The crease is the perpendicular bisector of segment AB because any point on the crease is equidistant from A and B, and by the conjecture, the set of equidistant - points is the perpendicular bisector of AB.