Question

marissa says that lines a and d will eventually intersect. is she correct? explain
o yes, because they are on the same plane
yes, because they are perpendicular
o no, because they are parallel
o no, because they are skew

Explanation:

Step1: Recall the properties of parallel lines

Parallel lines are lines in a plane that do not intersect.

Step2: Analyze the given lines

From the figure, lines \(a\) and \(d\) are in different planes. But in three - dimensional geometry, if two lines are parallel (they have the same direction vector in space), they will never intersect. Lines \(a\) and \(d\) are parallel (they have the same "slant" or direction in their respective planes' context).

Step3: Eliminate other options

• Lines \(a\) and \(d\) are not on the same plane (so "yes, because they are on the same plane" is wrong).
• Perpendicular lines intersect at a right - angle. Since they don't intersect, "yes, because they are perpendicular" is wrong.
• Skew lines are non - parallel and non - intersecting lines that are not in the same plane. But here lines \(a\) and \(d\) are parallel, so "no, because they are skew" is wrong.

Answer:

no, because they are parallel