Chapter 4.7, Problem 6ST3

To determine

To write: the theorem that allows to conclude that $B$ is on the perpendicular bisector of $\overline{AC}$ .

Answer to Problem 6ST3

If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.

Explanation of Solution

Given information:

In $\Delta ABC$ , $AB=7$ and $BC=7$ .

  

Calculation:

The theorem used is as follows:

If a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.

Here in $\Delta ABC$ , $AB=7$ and $BC=7$ , that is point $B$ is equidistant from the endpoints of segment $\overline{AC}$ , then point $B$ is on the perpendicular bisector of $\overline{AC}$ .