Parallel Lines, Skew Lines and Planes

These lessons help PreCalculus students learn about parallel lines, intersecting lines, skew lines and planes.

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The following figures show parallel lines, intersecting lines, perpendicular lines, and skew lines. Scroll down the page for examples and solutions.

Lines parallel perpendicular skew

Parallel And Skew Lines

Parallel lines are two lines in the same plane that remain at a constant distance from each other and never intersect. In a coordinate plane, parallel lines can be identified as having equivalent slopes. Parallel lines are traditionally marked in diagrams using a corresponding number of chevrons (or arrows).

Skew lines are two lines not in the same plane that do not intersect. Parallel and skew lines are also important concepts in Algebra and upper-level math courses.

What are intersecting and parallel lines?
Intersecting lines are coplanar.
Three points determine a plane.
Parallel lines never intersect and are coplanar.

What are skew lines?
Skew lines are noncoplanar and nonintersecting.

Learn what parallel, skew and intersecting lines are.
Parallel lines are two line in the same plane that do not intersect.

Skew Lines - Geometry Help
Students learn the definitions of parallel lines, skew lines.
Skew lines are non-coplanar lines that do not intersect.

Parallel Planes and Lines
In Geometry, a plane is any flat, two-dimensional surface. Two planes that do not intersect are said to be parallel. Parallel planes are found in shapes like cubes, which actually has three sets of parallel planes. The two planes on opposite sides of a cube are parallel to one another.

How to identify parallel lines, a line parallel to a plane, and two parallel planes?
Lines are parallel if they are in the same plane (coplanar) and so not intersect.
We us the symbol || to represent parallel lines.
To mark parallel lines in a diagram, we use arrows.

Two lines in the same plane either intersect or are parallel. If two lines intersect and form a right angle, the lines are perpendicular.

Skew lines are lines that are non-coplanar and do not intersect.

Two planes are parallel if they never intersect.
Two planes are perpendicular if they intersect and form a right angle.


  1. Identify 3 pairs of parallel planes.
  2. Identify 2 pairs of perpendicular planes.
  3. Identify 2 pairs of skew lines.

Difference between parallel lines and skew lines.
Parallel lines are two coplanar lines that never intersect.
Skew lines are lines that are not coplanar and can never intersect.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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