Question

if (overline{gj}congoverline{ij}) and (gh = 61), what is (hi)?
(hi=square)

Explanation:

Step1: Use the perpendicular bisector theorem

Since \( \overline{GJ}\cong\overline{IJ}\) and \( HJ\perp IG\) (the right - angle symbol indicates perpendicularity), by the perpendicular bisector theorem (if a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment), point \( H\) is on the perpendicular bisector of \( IG\).

Step2: Conclude the relationship between \( HI\) and \( GH\)

The perpendicular bisector theorem states that \( HI = GH\).

Answer:

\(61\)