Question

Complete each statement with the word always, sometimes, or never.

Two lines skew to a third line are skew to each other

Short answer

Two lines skew to a third line are sometimes skew to each other.

Step-by-step solution

Step 1. Definition

Skew lines are those lines which are noncoplanar. They are neither parallel nor intersecting.

Step 2. Draw the diagram

Draw the figures of different cases where in two lines are skew to a third line and observe whether they are skew to each other or not.

Step 3. State the explanation

Clearly, in figure two lines are skew to each other but in figure 2 and 3 two lines are not skew to each other because in both the cases lines are either coplanar or intersecting or both. So, if the two lines are skew to a third line, those two lines can intersect or be parallel or skew to each other.

Thus, it is clear that two lines skew to a third line may or may not be skew to each other.