Question

which line segment is a perpendicular bisector?

Explanation:

Step1: Recall the definition of a perpendicular bisector

A perpendicular bisector of a line segment is a line segment that is perpendicular to the given line segment and divides it into two equal parts.

Step2: Analyze the given triangle

In the given triangle, we observe that \( ZY = XY = 44\), and \(\angle ZYW=\angle XYW = 90^{\circ}\). Also, \(\angle VZY=\angle VXY = 25^{\circ}\). By the Hypotenuse - Leg (HL) congruence criterion for right - angled triangles (\(\triangle ZYW\) and \(\triangle XYW\) are right - angled at \(Y\), \(ZY = XY\), and \(YW\) is common), \(\triangle ZYW\cong\triangle XYW\). So \(WY\) bisects \(ZX\) (since \(ZY = XY\)) and \(WY\perp ZX\) (given \(\angle ZYW=\angle XYW = 90^{\circ}\)).

Answer:

\(WY\)