Question

2 fill in the blank 3 points
7.
name all the parallel segments.
gh ||
hi ||
gi ||

Explanation:

Step1: Check the mid - segment theorem

In a triangle, the mid - segment (a segment connecting the mid - points of two sides of a triangle) is parallel to the third side.
Since \(AG = GB = 4\), \(AH=\) (not directly needed here, but from the ratio of sides), \(HI\) is a mid - segment. \(GH\) is a mid - segment. \(GI\) is a mid - segment.
For \(GH\):
\(\frac{BG}{BA}=\frac{BH}{BC}=\frac{4}{4 + 4}=\frac{7}{7+7}=\frac{1}{2}\). By the converse of the basic proportionality theorem (Thales' theorem), \(GH\parallel AC\)

Step2: For \(HI\)

\(\frac{CH}{CB}=\frac{CI}{CA}=\frac{7}{7 + 7}=\frac{6}{6+6}=\frac{1}{2}\). By the converse of the basic proportionality theorem (Thales' theorem), \(HI\parallel AB\)

Step3: For \(GI\)

\(\frac{AG}{AB}=\frac{AI}{AC}=\frac{4}{4 + 4}=\frac{6}{6+6}=\frac{1}{2}\). By the converse of the basic proportionality theorem (Thales' theorem), \(GI\parallel BC\)

Answer:

\(GH\parallel AC\), \(HI\parallel AB\), \(GI\parallel BC\)