Question

In $△ABC$,$AB=7$ and $BC=7$. Write the theorem that allows you to conclude that $B$is on the perpendicular bisector of $\overline{\mathit{A}\mathit{C}}$.

Short answer

The theorem that justifies the statement that $B$is on the perpendicular bisector of$\overline{AC}$ is the theorem 4-6 which states that if a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.

Step-by-step solution

Step 1. Observe the diagram.

The diagram showing the triangle$ABC$ is:

Step 2. Write the theorem 4-6.

Theorem 4-6 states that if a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.

Step 3. Description of step.

It is being given that $AB=7$and $BC=7$.

Therefore, the point $B$ is equidistant from the endpoints of the segment $AC$.

Therefore, by using the theorem 4-6 it can be noticed that the point lies on the perpendicular bisector of $AC$.

Therefore, the theorem that justifies the statement that $B$is on the perpendicular bisector of $AC$ is theorem 4-6 which states that if a point is equidistant from the endpoints of a segment, then the point lies on the perpendicular bisector of the segment.