Question

if ∠ghj ≅ ∠ihj and gj = 26, what is ij? ij =

Explanation:

Step1: Apply the Angle - Bisector Theorem for Right Triangles

Since \( \angle GHJ\cong\angle IHJ\), \(HJ\) is the angle - bisector of \( \angle GHI\). Also, \( \angle JGH = \angle JIH=90^{\circ}\). By the Angle - Bisector Theorem for right triangles (if a ray bisects an angle of a right - angled triangle and is perpendicular to the opposite side, then it divides the opposite side into segments proportional to the adjacent sides. In the case of two right - angled triangles sharing a common angle - bisector \(HJ\), \(IJ = GJ\)).

Answer:

\(13\)