Question

construct arguments determine whether each statement is always, sometimes, or never true. justify your argument. lines ( a ) and ( b ) intersect at exactly one point. this is true only if lines ( a ) and ( b ) are coplanar and nonparallel.

Explanation:

In a plane (coplanar), two non - parallel lines will intersect at exactly one point. However, if the lines are parallel, they do not intersect. Also, in three - dimensional space, non - coplanar non - parallel lines (skew lines) do not intersect. But the statement does not specify the context. If we assume the general case of lines in a plane (which is a common assumption in basic geometry when not specified otherwise), the condition of being coplanar and non - parallel is considered.

Answer:

Sometimes, this is true only if lines \(a\) and \(b\) are coplanar and non - parallel.