Constructing a Parallel Line Using a Point Not on the Given Line

Constructing a Parallel Line Using a Point Not on the Given Line
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  • 0:07 Drawing a Parallel Line
  • 0:45 Tools Needed
  • 1:11 The Process
  • 3:51 Checking Your Work
  • 4:02 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson, and you will learn how to draw parallel lines with just a compass and a straightedge. Also, learn why you would want to be able to do this in real life.

Drawing a Parallel Line

When would you need to draw a pair of parallel lines, or a pair of lines that never intersect and are always the same distance apart? If you happened to be an architectural artist, or one of those people who draw up the blueprints for buildings and such, this skill would come in handy. Just think of all the situations where parallel lines are a must. The walls in hallways must be parallel; otherwise, you would end up with a hallway that got smaller and smaller until nobody could fit inside.

The method that I am going to show you is a sure-fire way to draw a pair of parallel lines. And you don't even need to use a ruler.

Tools Needed

All you need is a straightedge of some sort and a compass. The straightedge can be the edge of a hardcover book or even the edge of a piece of cardstock. The compass is not the kind that tells you which direction you're facing, but the math tool that you use to draw arcs and circles. With just these two drawing/math tools, you can draw lines that are definitely parallel.

The Process

The process is simple. And I am glad that you are watching this process rather than reading about it. It makes much more sense seeing it in action rather than just seeing it in print. So, here goes. If you can follow along with your own paper and tools, that would be great so you can get a feel for how it works.

1. (See the video starting at 01:26 for this step.) The first step is to draw your line and point. Draw your point somewhere not on the line. I usually draw the point above the line somewhere. I'm going to label my line and point to make referring to them easier. I am going to make two dots on either end of my line and label them A and B. I am going to label my point C. So, now I have my line AB and my point C.

Step 1
drawing a parallel line

2. (See the video starting at 01:59 for this step.) Next, I am going to draw a transverse, or a line that crosses two other lines. To do this, I take my straightedge and draw a transverse through my point C and intersecting my line AB. I've drawn the transverse at an angle, and I would recommend you do this all the time instead of drawing a transverse that is perpendicular to your line. At this point, the transverse is only crossing my one line, but I am going to use this transverse to create my second line. The point where my transverse intersects my line I am going to label D.

Step 2
drawing a parallel line

3. (See the video starting at 02:31 for this step.) Now I am going to take my compass and place one end of the compass on point D. I set the width to a distance roughly half of the distance between points D and C. I draw an arc that crosses my line AB and my transverse. Then I move the compass to point C, keeping the width the same. I draw a similar arc from point C. I now have two arcs that look similar to each other.

Step 3
drawing parallel lines

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