Question

Why does the perpendicular bisector of a segment construction work? Which theorem, postulate, or definition is used?

A. Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment.
B. Isosceles Triangle Definition
C. There is exactly one line that is going through a given point and perpendicular to a given line.
D. If a point is equidistant from the endpoints of a segment, then it's sitting on the perpendicular bisector of the segment.

Answer 1

Answer:

The answer you're looking for is D.

Step-by-step explanation:

If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment. This is called the Perpendicular Bisector Theorem.

Answer 2

Answer:

Perpendicular Bisector Theorem Converse

Step-by-step explanation:

The perpendicular bisector of a segment construction works because of -

Perpendicular Bisector Theorem Converse: If a point is equidistant from the endpoints of a segment, then the point is on the perpendicular bisector of the segment.

A. Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. This is the definition of Perpendicular Bisector Theorem.

We usually assume the opposite to prove something. So, taking the converse of a definition and proving the definition is right, is the correct way to do so.