Parallel Lines
Transcript Start

This lesson covers parallel lines. 

Parallel lines are two lines in the same plane that are always the same distance apart and never intersect or touch.

Let’s look at this table top. It is a perfectly flat surface, and if we pretend that it has no thickness and extends infinitely, in all directions, we can call it a plane. Place a piece of paper shaped like a rectangle, that is not a square, on top of the table, and let’s examine it. It has two sides that are longer, and two sides that are shorter.

Imagine extending the two longer sides, infinitely, in either direction to form lines. These two lines are parallel to each other. Imagine extending the two shorter sides, infinitely, in either direction. These two lines are also parallel to each other. 

Let's take the same piece of paper and carefully fold it in half, width wise, or horizontally, in this case. Make a good crease, and without opening it up, fold the paper, yet again, with the same orientation. Make a good crease, and then unfold the paper. The creases that you just formed, created three new lines that are parallel to the shorter sides of the paper.

Use any accessible ruler or a tactile caliper to show that any two of these two parallel lines are always the same distance apart. Now we are going to draw our own.

We are going to use a piece of paper to represent our plane and draw two lines that are parallel. One line will be labeled "l" and the other "m". Notice that each line has an arrowhead at each "end" 
indicating that it extends infinitely in both directions.

You could adapt this figure for a student with low vision by simply ensuring that you had good contrast between the lines and the plane and placing them both on a well-lit, and contrasting additional drawing surface. You could use a black-line marker such as a Sharpie, 20/20 pen, or Flair pen on a white piece of paper. I would also use a straightedge to ensure that the two lines are as straight as possible.

You could adapt this figure for a student who is blind by using, one; a piece of braille paper placed on a rubber pad, a clipboard with craft foam, or a Sewell Raised Line Drawing Board– basically a clipboard with a rubberized surface already attached for your plane, and a tracing wheel for your drawing tool. The drawing would appear raised on the opposite side of the working area, so you would need to turn it over and then label it appropriately using a braillewriter, slate & stylus, or brailled, peel-and-feel labels. I would also use a straightedge.

Or, number two; a piece of special film placed on either an APH Draftsman, or an EASY inTACT Sketchpad, and the accompanying stylus for a drawing tool. The drawing will appear raised on the drawing surface of the film. The drawing can then be labeled using a braillewriter, slate and stylus, or brailled peel-and-feel labels, although it is not easy inserting the film into a braillewriter. I would also use a straightedge.

Or, three; any other method you may devise to accomplish a similar effect.

The student would be able to create this same figure independently using the above methods, and should be encouraged to do so, as creating their own graphics, in addition to reading them, reinforces the math concept.

If the student is transitioning from print to braille, the use of a black line master on Swell Touch paper, run through a tactile graphics machine, such as the Zychem or PIAF, is highly encouraged.

Now, we are going to look at two non-parallel lines. These two lines labeled "p" and "q" are not parallel because they intersect.

These two non-parallel lines could be created for a student with low vision and for a student who is blind as outlined above.

If we go back to our original picture of our two parallel lines labeled "l" and "m", we have a special symbol in mathematics to indicate that they are parallel. It is two parallel, vertical line segments, which is very appropriate in print. We have an equally appropriate symbol for students who read braille. In the Nemeth code it is dots 1,2,4,6 followed by dots 1,2,3. In UEB it is dots 3,4,5,6 followed by dots 1,2,3.

We can extend our work with parallel lines to the Cartesian coordinate plane. So, let’s look at two parallel lines in the coordinate plane. The slopes of these two lines is two-thirds. We can generalize this to any pair of parallel lines in the coordinate plane. Parallel lines have the same slope.

You could adapt this figure for a student with low vision by simply ensuring that you had good contrast between the lines, the axes, and the gridlines of the coordinate plane, and placing them both on a well-lit and contrasting additional drawing surface. You could use a black-line marker such as a Sharpie, 20/20 pen, or Flair pen. I would also use a straightedge to ensure that the two lines are drawn as straight as possible. You could purchase already prepared bold-line graph paper or create it yourself.

You could adapt this figure for a student who is blind by using, one; the APH Graphic Aid for Mathematics-- rubber graph board, push pins, thumb tacks, and rubber bands.

Or, two; raised-line graph paper on a cork board, push pins, thumb tacks, and rubber bands.
Or, three; any other method you may devise to accomplish a similar effect.

The student would be able to create this same figure independently using the above methods and should be encouraged to do so, as creating their own graphics, in addition to reading them, reinforces the math concept.

If your student still has difficulties with understanding the concept of parallel lines, you might wish to describe certain real life examples of parallel lines, such as train tracks or parallel streets in a city grid pattern. Have the student examine a real train track if possible or at least a wooden toy train on tracks. 

Have the student’s Orientation & Mobility Specialist reinforce the concept of parallel streets during a mobility run or at least use something like the APH Picture Maker Wheatley Tactile Diagramming Kit to construct parallel streets on a tactile map.

In this video, we have covered the definition of parallel lines, how to draw them in the plane, including a coordinate plane, and how to write parallel in mathematical notation.