Question

using the side - splitter theorem, which segment length would complete the proportion?
\\( \frac { g h } { h e } = \frac {? } { j f } \\)
\\( \bigcirc g f \\)
\\( \bigcirc j h \\)
\\( \bigcirc g j \\)
\\( \bigcirc e f \\)

Explanation:

Step1: Recall the Side - Splitter Theorem

The Side - Splitter Theorem states that if a line is parallel to one side of a triangle and intersects the other two sides, then it divides those sides proportionally.
In the given figure, assume the line \(HJ\) is parallel to \(EF\). Then for \(\triangle GEF\), we have \(\frac{GH}{HE}=\frac{GJ}{JF}\)

Answer:

C. \(GJ\)