Question

what additional information would you need to conclude that \overleftrightarrow{de} is the perpendicular bisector of \overline{ac}?

Explanation:

Step1: Recall Perpendicular Bisector Definition

A perpendicular bisector of a segment is a line that is perpendicular to the segment and divides it into two equal parts. So, we need \( DE \perp AC \) (which seems to have a right angle marked, so maybe \( AB = BC \) or \( B \) is the midpoint).

Step2: Identify Missing Condition

From the diagram, we know \( DE \) is perpendicular to \( AC \) (right angle at \( B \)). To be a bisector, \( B \) must be the midpoint of \( \overline{AC} \), so we need \( AB = BC \) (or \( B \) is the midpoint, i.e., \( AB = BC \)).

Answer:

We need to know that \( AB = BC \) (or that \( B \) is the midpoint of \( \overline{AC} \)), meaning \( DE \) divides \( \overline{AC} \) into two equal segments (along with being perpendicular).