Question

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

Two lines that are not coplanar intersect.

Short answer

Two lines that are not coplanar never intersect.

Step-by-step solution

Step 1. Definition

Coplanar lines are those lines which lies in the same plane.

Step 2. Draw a diagram

Consider two planes such that they two lines are not coplanar and do not intersect.

Step 3. State the explanation

For two intersecting non-coplanar lines, take the point of intersection as A, and one other point on each line. Since, the lines intersect the three points are not colinear. Therefore, all three are in exactly in one plane. That means each line has two points in that plane, so each line is in that plane, therefore they are coplanar. But this contradicts the assumption that the lines were not coplanar. So, the assumption that non-coplanar lines intersect is wrong.

Therefore, two lines that are not coplanar never intersect.