Skew Lines
Transcript Start
This lesson covers skew lines. Skew lines are two lines that are not coplanar. Also skew lines cannot intersect because if they did intersect, they would be coplanar. One of the most popular examples of skew lines in the real world are probably the flight paths of airplanes. If one has vision, you encounter this phenomenon all the time. You look up in the air and see two airplanes in the sky that look like they are about to crash because it appears that their flight paths are going to intersect. However, they easily avoid each other, because they are, in actuality, in separate planes. The planes are not coplanar.
You could adapt this image for a student with low vision, or who is blind, by simply guiding their own straightened arms across each other with one above the other stating that the right arm represents one airplane, and the left arm another airplane. They can understand how the one arm can pass above the other without contact or intersection.
Another method would be to use two taught rods or sticks of some sort.
Another real world example is highway overpasses. If you were bold, you could adapt this image for a student with low vision, or who is blind, by actually driving them out to such a set of overpasses, and letting them hear the traffic traveling directly above, or below them. Then again, constructing the tangled image out of an erector set, or LEGOs, or even Tinker Toys might be fun for all!
One of the simplest examples of a pair of skew lines is the pair of lines through opposite edges of a regular tetrahedron. There are six edges in a regular tetrahedron. One. Two. Three. Four. Five. Six.
If you look at one edge you will notice that it intersects with four other edges. One. Two. Three. Four. Therefore, it’s opposite edge is the one which it does not intersect, and thus the lines through these edges are skew lines.
You will notice that I used Geometro pieces from the APH collection. These are also available directly from Geometro in Canada, if you live outside the United States. I love these tools so much that I would use them with all students; sighted and those with a visual impairment. You can always use a plastic or paper-made tetrahedron and straws or sticks to demonstrate this concept, but I highly recommend that you use something that allows the student to manipulate the tetrahedron, and yet have the simulated lines stick to the edges.
The most common demonstration of skew lines is done with a box or rectangular prism, which can be found just about anywhere. You could use a facial tissue box, a toothpaste container, or plastic, ready-made, rectangular prism.
However, I will again use a Geometro box or in this case a cube and hook material rods to demonstrate several skew lines on this cube.
I will start by reviewing parallel lines - two lines in the same plane that are always the same distance apart and never intersect or touch. These lines are parallel.
Next, let’s find a few perpendicular lines - lines that intersect to form right angles. These lines are perpendicular.
Finally, we are looking for skew lines - two lines that are not coplanar. These lines are coplanar.
What is extremely nice about the Geometro model is that they can easily be unfolded and refolded, over and over again, by any student, but especially one who is blind, or has low vision.
I will conclude with one classic paper and pencil demonstration of skew lines. We have a 2D drawing of a 3D figure, demonstrating a line CD stabbing the plane which contains the line AB, but the two lines do not intersect.
You could adapt this image for a student with low vision, or who is blind, by simply taking a piece of paper with a line AB already drawn on it with a black marker and/or a tracing wheel so that it is raised and then stabbing it with a pencil, which you can indicate is line CD such that it does not intersect the line AB.
In this video, we have covered the definition of skew lines, and how to find them in the real world, and using various geometric 3D figures.