Parallel, Intersecting, and Skew Lines

In 2D geometry, lines are either parallel or intersecting. When a third dimension is added, lines that are not parallel often never intersect. These non-intersecting, non-parallel lines are called skew lines.

The relationships of lines in three dimensions are explored in the Parallel, Intersecting, and Skew Lines Gizmo. A slowly rotating 3D graph space is shown on the right of the Gizmo. Students and teachers can change the speed and orientation of the 3D simulation. Viewing the graph from a number of different angles makes 3D graphs easier to understand. Throughout the lesson materials, students are encouraged to recall previous knowledge from 2D geometry and extend that knowledge into the 3rd dimension.