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Geometry: High School15 chapters | 160 lessons

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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.

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.

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 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.

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.

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.

4. (See the video starting at 03:03 for this step.) Now I'm going to set the width of the compass to the distance between the two intersections of the bottom arc. The bottom intersects the transverse and the line AB. I want to set my compass to the distance between these two intersections. Once I've set the width of the compass, I move my compass to the upper arc and place one point where the arc intersects with the transverse, and then I draw a little arc that intersects the upper arc. This new point I will label E.

5. (See the video starting at 03:36 for this step.) To finish, I take my straightedge and draw a line through points C and E. This new line will be parallel to my line AB.

To check your work, you can use a ruler to see if the distance between the two lines remains the same no matter where you measure. Just make sure you are measuring perpendicular to both lines.

Let's recap what we've learned so far. We've learned that drawing **parallel lines**, lines that never intersect and are always the same distance apart, is a useful skill for architectural artists when making blueprints. We learned that all you need is a straightedge and a compass to draw a pair of parallel lines. Only a few steps are required.

You start off with a line and a point somewhere not on the line. You then draw a **transverse**, a line that crosses two other lines, through the point that intersects the line at an angle. You then draw two arcs, one from the point and the other from where the transverse intersects the line. The arcs will intersect both a line and the transverse, and you can see this in the lower arc. You measure that distance with your compass, and you mark that distance on the upper arc. You then finish by drawing a line through your original point and the new point you just created by marking the upper arc with a little arc. You can check your work by checking to see if the distance between the two lines remains consistent.

After reviewing this lesson, you'll have the ability to:

- Define parallel lines
- Explain how to draw parallel lines with a straightedge and a compass
- Identify how to check your work when drawing parallel lines with this method

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Geometry: High School15 chapters | 160 lessons

- Angles Formed by a Transversal 7:40
- Parallel Lines: How to Prove Lines Are Parallel 6:55
- Using Converse Statements to Prove Lines Are Parallel 6:46
- Constructing a Parallel Line Using a Point Not on the Given Line 5:15
- What Are Polygons? - Definition and Examples 4:25
- Regular Polygons: Definition & Parts 6:01
- How to Find the Number of Diagonals in a Polygon 4:49
- Finding the Perimeter of Polygons 5:19
- Measuring the Area of Regular Polygons: Formula & Examples 4:15
- Measuring the Angles of Triangles: 180 Degrees 5:14
- How to Measure the Angles of a Polygon & Find the Sum 6:00
- Go to High School Geometry: Parallel Lines and Polygons

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