Error: See solution. Correct statement: If two lines do not intersect and are coplanar, then they are parallel.
Practice makes perfect
In a Cartesian coordinate system, which only has two dimensions, the statement would be true.
This is because these lines are on one and the same plane! If we broaden our perspective and think in three-dimensional space, it is possible for two lines to not intersect and not be parallel. Such lines are known as skew lines. Below we see an example.
Therefore, the statement should be changed to
&If two lines do not intersect and are coplanar,
&then they are parallel.
