Question

∠fjh is a right angle and \\(\overline{ij} \cong \overline{fj}\\).

which term describes \\(\overline{hj}\\)?

perpendicular bisector \t median

altitude \t none of these

Explanation:

Step1: Recall Definitions

• Perpendicular Bisector: A line that is perpendicular to a segment and bisects it (divides into two equal parts).
• Median: A segment from a vertex to the midpoint of the opposite side.
• Altitude: A segment from a vertex perpendicular to the opposite side (or its extension).

Step2: Analyze Given Information

• $\angle FJH$ is a right angle, so $\overline{HJ} \perp \overline{FJ}$.
• $\overline{IJ} \cong \overline{FJ}$, so $J$ is the midpoint of $\overline{FI}$ (since $IJ = FJ$, $J$ divides $FI$ into two equal parts).

Step3: Match with Definitions

• Since $J$ is the midpoint of $\overline{FI}$ and $\overline{HJ} \perp \overline{FI}$ (because $\angle FJH$ is right, so $\overline{HJ} \perp \overline{FJ}$ and $\overline{FJ}$ is part of $\overline{FI}$), $\overline{HJ}$ is perpendicular to $\overline{FI}$ and bisects it. Thus, it is a perpendicular bisector.

Answer:

perpendicular bisector