Question

∠eif is a right angle and ( overline{hi} cong overline{ei} ).
which term describes ( overline{fi} )?
perpendicular bisector angle bisector
altitude none of these

Explanation:

Step1: Recall definitions

• Perpendicular bisector: A line that is perpendicular to a segment and bisects it.
• Angle bisector: A line that divides an angle into two equal parts.
• Altitude: A segment from a vertex of a triangle perpendicular to the opposite side.

Step2: Analyze the given information

We know that \(\angle EIF\) is a right - angle and \(HI\cong EI\). But there is no information to suggest that \(FI\) is a perpendicular bisector (we don't know if \(FI\perp HE\) and bisects \(HE\) in a non - trivial way related to the perpendicularity condition for a bisector in the context of triangle properties), no information that \(FI\) bisects an angle (no angle - splitting information given in terms of angle measures) and no information that \(FI\) is an altitude (altitude is from a vertex of a triangle to the opposite side, and there is no clear triangle - vertex - to - opposite - side relationship here for the definition of an altitude).

Answer:

none of these