Question

look at the diagram.
which term describes \\(\overline{gi}\\)?
perpendicular bisector
median
angle bisector
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.
• Angle Bisector: A line that divides an angle into two equal parts.
• Right Angle: Indicated by the red square, so \( \overline{GI} \perp \overline{HJ} \) (since \( \angle GIH = 90^\circ \)).

Step2: Check Segment Lengths

• Length of \( HI = 68 \), length of \( IJ = 54 \). Since \( 68

eq 54 \), \( I \) is not the midpoint of \( HJ \). So \( \overline{GI} \) is not a perpendicular bisector (as it doesn't bisect \( HJ \)) or a median (since median requires midpoint).

• There's no indication \( \overline{GI} \) bisects an angle (no equal angles shown related to angle bisector).

Step3: Conclusion

Since \( \overline{GI} \) is perpendicular to \( HJ \) but doesn't bisect \( HJ \), isn't a median, and isn't an angle bisector, the term is "none of these".

Answer:

none of these