Question

in the rectangular prism shown below, which lines are parallel? select all that apply.

Explanation:

Step1: Recall the definition of parallel lines

Parallel lines are lines in a plane that do not intersect. In a rectangular prism, edges that are in the same direction (either length, width, or height) are parallel.

Step2: Analyze each pair

• For \(\overleftrightarrow{DG}\) and \(\overleftrightarrow{EF}\): Both are edges of the base (width - like direction), so they are parallel.
• For \(\overleftrightarrow{IJ}\) and \(\overleftrightarrow{EF}\): \(\overleftrightarrow{IJ}\) is on the top - face (width - like) and \(\overleftrightarrow{EF}\) is on the bottom - face (width - like), they are parallel.
• For \(\overleftrightarrow{FJ}\) and \(\overleftrightarrow{GK}\): Both are height - like edges, so they are parallel.
• For \(\overleftrightarrow{HK}\) and \(\overleftrightarrow{IJ}\): \(\overleftrightarrow{HK}\) is on the top - face (length - like) and \(\overleftrightarrow{IJ}\) is on the top - face (width - like), they are parallel.

Answer:

\(\overleftrightarrow{DG}\) and \(\overleftrightarrow{EF}\), \(\overleftrightarrow{IJ}\) and \(\overleftrightarrow{EF}\), \(\overleftrightarrow{FJ}\) and \(\overleftrightarrow{GK}\), \(\overleftrightarrow{HK}\) and \(\overleftrightarrow{IJ}\)