Question

question 18 (5 points)
listen
the figure is a rectangular prism. identify which one of the line segments in the given figure is perpendicular to \\(\overline{hg}\\).
a) \\(\overline{bf}\\)
b) \\(\overline{ef}\\)
c) \\(\overline{fg}\\)
d) \\(\overline{bc}\\)

Explanation:

Step1: Recall Perpendicular Definition

In a rectangular prism, adjacent edges meet at right angles (perpendicular).

Step2: Analyze $\overline{HG}$

$\overline{HG}$ is an edge of the top face (EFGH). Edges meeting $\overline{HG}$ at vertex H or G should be checked. At G, $\overline{FG}$ and $\overline{HG}$ are adjacent edges of the face FGHG (a rectangle), so they are perpendicular.

Step3: Eliminate Other Options

• Option A: $\overline{BF}$ is vertical, not perpendicular to horizontal $\overline{HG}$.
• Option B: $\overline{EF}$ is parallel to $\overline{HG}$, not perpendicular.
• Option D: $\overline{BC}$ is vertical, not perpendicular to $\overline{HG}$.

Answer:

C) $\overline{FG}$