Question

if ∠hik ≅ ∠jik and jk = 29, what is hk?
hk =

Explanation:

Step1: Apply the Angle - Bisector Theorem (or the property of a point on the angle bisector)

A point \(K\) is on the bisector of \(\angle HIJ\) (\(\angle HIK\cong\angle JIK\)), and \(KJ\perp IJ\), \(KH\perp IH\). According to the property that if a point is on the bisector of an angle, then it is equidistant from the sides of the angle.

Step2: Relate the lengths of \(HK\) and \(JK\)

Since \(K\) is on the bisector of \(\angle HIJ\), and \(KJ\) and \(KH\) are the perpendicular distances from \(K\) to the sides \(IJ\) and \(IH\) of \(\angle HIJ\) respectively. So \(HK = JK\).

Answer:

\(29\)