Question

consider the lines that contain the segments in the figure and the planes that contain the faces of the figure. choose the pairs of parallel lines.

Explanation:

Step1: Recall parallel - line definition

Parallel lines in 3 - D are lines that do not intersect and are in the same plane.

Step2: Analyze the cube's edges

In a cube, for example:

• Line $AB$ is parallel to line $CD$ because they are in the same plane (top - face plane) and do not intersect.
• Line $AB$ is also parallel to line $HG$ because they are in parallel planes (top - face and bottom - face) and have the same direction.
• Line $AD$ is parallel to line $BC$ (in the top - face plane), line $AD$ is parallel to line $EH$ (in parallel planes).
• Line $AE$ is parallel to line $BF$, line $AE$ is parallel to line $DH$, line $CG$ is parallel to line $BF$, line $CG$ is parallel to line $DH$.

Answer:

$AB\parallel CD$, $AB\parallel HG$, $AD\parallel BC$, $AD\parallel EH$, $AE\parallel BF$, $AE\parallel DH$, $CG\parallel BF$, $CG\parallel DH$