Question

use the figure and the given information to find the indicated measure. \overleftrightarrow{zx} is the perpendicular bisector of \overline{wy}, and yz = 13.75. find wz. wz = \square

Explanation:

Step1: Recall Perpendicular Bisector Property

A perpendicular bisector of a segment is a line that is perpendicular to the segment and divides it into two equal parts. Also, any point on the perpendicular bisector is equidistant from the endpoints of the segment. Here, \( \overleftrightarrow{ZX} \) is the perpendicular bisector of \( \overline{WY} \), so point \( Z \) is on the perpendicular bisector of \( \overline{WY} \). This means \( ZW = ZY \) (by the Perpendicular Bisector Theorem, which states that any point on the perpendicular bisector of a segment is equidistant from the segment's endpoints).

Step2: Substitute the Given Value

We are given that \( YZ = 13.75 \). Since \( ZW = ZY \) (from the Perpendicular Bisector Theorem), we can conclude that \( WZ = YZ \). So, substituting the value of \( YZ \), we get \( WZ = 13.75 \).

Answer:

\( 13.75 \)