Question

for exercises 1 - 3, use the figure at the right. question 1 1 pts which line segment is parallel to \\( \overline { g e } \\) ? \\( \overline { k i } \\) \\( \overline { d h } \\) \\( \overline { h i } \\) \\( \overline { f g } \\)

Explanation:

Step1: Recall the property of parallel lines in a rectangular prism

In a rectangular prism, opposite edges are parallel.

Step2: Analyze each option

• For \(\overline{KI}\): In the rectangular prism, \(\overline{GE}\) and \(\overline{KI}\) are opposite edges of the top - front and bottom - back faces respectively. They are parallel.
• For \(\overline{DH}\): \(\overline{DH}\) is perpendicular to \(\overline{GE}\) (they are in different directions in 3 - D space).
• For \(\overline{HI}\): \(\overline{HI}\) is perpendicular to \(\overline{GE}\) (they are in different directions in 3 - D space).
• For \(\overline{FG}\): \(\overline{FG}\) is adjacent to \(\overline{GE}\) (they meet at a vertex \(G\)) and are not parallel.

Answer:

\(\overline{KI}\)