Question

in the cube shown below, which lines are parallel?

Explanation:

Step1: Recall the definition of parallel lines

Parallel lines are lines in a plane that do not intersect. In a cube, edges that are in the same direction and do not meet are parallel.

Step2: Analyze each pair

• For \(\overleftrightarrow{LM}\) and \(\overleftrightarrow{KO}\):

In a cube, \(LM\) and \(KO\) are both in the same direction (horizontal - like in their respective planes). They do not intersect.

• For \(\overleftrightarrow{JK}\) and \(\overleftrightarrow{LM}\): \(JK\) is vertical (assuming standard cube orientation) and \(LM\) is horizontal. They are not parallel.
• For \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{IM}\): \(HI\) and \(IM\) meet at point \(I\), so they are not parallel.
• For \(\overleftrightarrow{HI}\) and \(\overleftrightarrow{HK}\): \(HI\) and \(HK\) meet at point \(H\), so they are not parallel.

Answer:

\(\overleftrightarrow{LM}\) and \(\overleftrightarrow{KO}\)