Question

use the image to answer the questions below. assume segments and planes that appear to be parallel or perpendicular are parallel or perpendicular, respectively.
part 1 of 3
(a) name two segments that are skew to \\( \overline { h g } \\).
and
part 2 of 3
(b) name two segments that are skew to \\( \overline { b c } \\).
and

Explanation:

Part 1 of 3

Step 1: Recall the definition of skew lines

Skew lines are non - parallel and non - intersecting lines in 3 - D space.

Part 2 of 3

Step 1: Recall the definition of parallel lines

Parallel lines are lines in a plane that do not intersect and have the same direction.

Step 2: Identify segments parallel to \(\overline{BC}\)

In a rectangular prism, opposite sides of the rectangular faces are parallel.
For segment \(\overline{BC}\), we look at the other edges of the rectangular faces.
The segment \(\overline{FG}\) is parallel to \(\overline{BC}\) (since \(BCGF\) is a rectangle) and \(\overline{EH}\) is parallel to \(\overline{BC}\) (since \(BCDE\) and \(EFGH\) are rectangles and the translation from one face to the other gives parallelism).

Part 3 of 3

Step 1: Recall the definition of perpendicular lines

Perpendicular lines are lines that intersect at a right angle (\(90^{\circ}\)).

Step 2: Identify segments perpendicular to \(\overline{HG}\)

In the rectangular prism, if we consider the edges meeting at the vertices of the edge \(\overline{HG}\).
The segment \(\overline{GF}\) is perpendicular to \(\overline{HG}\) (since \(FGH\) is a right - angled corner of the rectangular face \(FGH E\)) and \(\overline{HE}\) is perpendicular to \(\overline{HG}\) (since \(EHG\) is a right - angled corner of the rectangular face \(EHGF\)).

Answer:

• Parallel to \(\overline{BC}\): \(\overline{FG}\), \(\overline{EH}\)
• Perpendicular to \(\overline{HG}\): \(\overline{GF}\), \(\overline{HE}\)