Question

1. match.

given: \\( \angle d e f ; \overrightarrow{e i} \\) bisects \\( \angle d e f ; g i=3 \\) in
what is the length of \\( h i \\) ?
by which theorem?

Explanation:

Step1: Recall the Angle Bisector Theorem

The Angle Bisector Theorem states that if a point is on the bisector of an angle, then it is equidistant from the sides of the angle.

Step2: Apply the theorem

Since \(EI\) bisects \(\angle DEF\), and \(GI\perp ED\), \(HI\perp EF\), by the Angle Bisector Theorem, \(HI = GI\).

Step3: Substitute the given value

Given \(GI = 3\) in, so \(HI=3\) in.

Answer:

The length of \(HI\) is \(3\) in. By the Angle Bisector Theorem.