Question

1. determine if each statement is sometimes, always, or never true.

two lines that intersect in one point are a sometimes b always c never coplanar.
two lines that never intersect are a sometimes b always c never coplanar.

Explanation:

First Statement

Step1: Analyze the nature of intersecting lines

If two lines intersect at a point, then by the definition of coplanar (lying on the same plane), we can construct a plane that contains both lines. So two lines that intersect in one point are always coplanar.

Second Statement

Step1: Consider different cases of non - intersecting lines

Parallel lines (which are non - intersecting) are coplanar. But skew lines (non - intersecting and non - parallel) are not coplanar. So two lines that never intersect are sometimes coplanar.

Answer:

1. B. always
2. A. sometimes