Question

1. choose the best answer. which line is a segment bisector?

$overleftrightarrow{xz}$
$overline{ac}$
$overleftrightarrow{ac}$
$overleftrightarrow{yc}$

Explanation:

Step1: Recall the definition of a segment bisector

A segment bisector is a line, ray, or segment that divides a line segment into two equal parts.

Step2: Analyze each option

• For \(\overleftrightarrow{XZ}\): Since \(\overline{AY}\cong\overline{YC}\), and \(\overleftrightarrow{XZ}\) passes through the mid - point \(Y\) of \(\overline{AC}\), it divides \(\overline{AC}\) into two equal parts.
• For \(\overline{AC}\): It is a line segment, not a bisector of another segment.
• For \(\overleftrightarrow{AC}\): It is a line that contains the segment \(\overline{AC}\), but it does not bisect another segment.
• For \(\overleftrightarrow{YC}\): It is a ray, and it does not bisect the segment \(\overline{AC}\) (it is just a part of the line that contains the mid - point).

Answer:

\(\overleftrightarrow{XZ}\)