Question

what is gj?
gh is 9, there are right angles at h and j, and angle at i is bisected. gj = \square

Explanation:

Step1: Apply the Angle - Bisector Theorem for Distances

If a point lies on the bisector of an angle, then it is equidistant from the two sides of the angle. Here, point \(G\) lies on the bisector of \(\angle H IJ\) (\(GI\) is the angle - bisector), \(GH\perp HI\) and \(GJ\perp IJ\).

Step2: Use the property of equidistant

By the angle - bisector property, \(GH = GJ\). Given \(GH = 9\).

Answer:

\(9\)