Question

complete the following statement. d ⊥ e and e ⊥ f so d ? f assume all lines are coplanar. neither, they are skew lines ⊥ ∥

Explanation:

Step1: Recall the property of perpendicular lines in a plane

In a plane, if two lines are both perpendicular to a third line, then the two lines are parallel to each other. Mathematically, if \(d\perp e\) and \(e\perp f\) (where all lines are coplanar), we can use the theorem about perpendicular and parallel lines in a plane.

Step2: Apply the property to the given lines

Given \(d\perp e\) and \(e\perp f\) with all lines coplanar, by the property of perpendicular lines in a plane, \(d\) and \(f\) must be parallel to each other. So the relationship between \(d\) and \(f\) is \(\parallel\).

Answer:

\(\boldsymbol{\parallel}\) (the third option: \(\boldsymbol{\parallel}\))