Introduction: How to Construct Two Parallel Lines

Picture of How to Construct Two Parallel  Lines

Drawing parallel lines without a ruler can be hard. Here, i show you how with just a straightedge and a compass. (NO RULERS)

Step 1: Step One

Picture of Step One

The first thing you do is draw a straight line. It can be any length. Then draw a point above the line.

Step 2: Steps Two & Three

Picture of Steps Two & Three

Place the stylus of the compass on the point, and swing the compass down to make two marks on the line. These points of intersection are equidistant from the original point. Then, draw marks below the line, by placing the stylus on the points of intersection. Draw a line from where these two meet to the original point (the red arrow marks this)

Step 3: Step Four & Five

Picture of Step Four & Five

Mark two points on the 2nd line by placing the compass stylus on the original (red arrow) dot, and swinging it down and up. Then, swing the compass from both of these new pointsof intersection , on either side of the line, to form 2 new points.

Step 4: Step Five

Picture of Step Five

Connect these 3 points, and now you have 2 parallel lines! The original line and the most recently made are parallel with each other. This is because you formed 2 perpendicular lines, which are 90 degrees each. The 90 degrees x2 equals 180 degrees, therefore producing parallel lines.


ilpug (author)2011-11-11

Simpler method- make two circles of equal diameter, centered on the first line segment. Then, put a point at the most extreme edge of those circles on the same side of the line. Draw a line segment through those two points, so that it is tangential to the two circles and parallel to the other line segment.

iceng (author)2011-10-30

Impressive publishing waterfall event.

Parallel line segments is the description you should be talking about.

Any math teacher will tell you a line goes to + and - infinity.

Your reader,


Higgs Boson (author)iceng2011-11-05

Yeah. You bring up an interesting point, but the definition of parallel lines is, two lines that have the same slope but a different Y-intersect. Which means that even lines going on forever will still be parallel. And if you are talking about the fact that only segments are drawn than you must understand that infinities do not exist in nature so it would be impossible to draw. The segments that are drawn represent the theoretical concept of infinite lines using arrows (which can be seen on the final step).

iceng (author)Higgs Boson2011-11-06

The axiom in non-Euclidian Geometry is that parallel lines intersect at infinity.

Higgs Boson (author)iceng2011-11-06

But infinities do not exist in the natural world so it is irrelevant.

iceng (author)Higgs Boson2011-11-06

Not to my lack of understanding ;-)

Even Einstein speaks to infinity ;
"Two things are infinite: the universe and human stupidity;
and I'm not sure about the the universe."

Higgs Boson (author)iceng2011-11-06

Even so infinities do not exist outside of the conceptual world, other wise the problems of getting infinities as solutions to equations for quantum gravity would not be a problem. Either way geometric constructions are part of Euclidean Geometry, so the axiom for non-Euclidean geometry may not apply.

iceng (author)Higgs Boson2011-11-06

And further so, as a Electronic Engineer and Scientist I use "i" which is the representation of the square root of minus one  (-1)½ ...
That is an imaginary number used in Real-World electrical solutions.

You are polite and young man of 14 still to go through a lot
of matriculation,  Allow me to suggest a modicum of open
mindedness about our Wonderful World and high level concepts. 
Do you know there are more scientific papers of note being produced
and published then any one person can review in a lifetime.

Infinity is a fun target after a googleplexing some numbers.

Higgs Boson (author)iceng2011-11-07

wow you are very cool! I have been waiting for a very long time to have a conversation about math like that. I accept defeat. I think that open mindedness is something that I need to work on. thank you for the advice, and for having this conversation with me. I hope we can discuss this type of thing again sometime.

iceng (author)Higgs Boson2011-11-07

It was fun.
I am still liking your very clear, succinct and correct definition of parallel lines,
better then I remember in my geometry class ages ago.

freeza36 (author)iceng2011-11-07

I agree with Higgs. Thanks for pointing this out, and no hard feelings.

Higgs Boson (author)iceng2011-11-07

The more I think about the axiom you said, the more it seems to make sense. if the lines had a known different slope they would intersect at a finite distance, but if they had the same slope it would take an infinite distance for them to intersect.

freeza36 (author)Higgs Boson2011-11-06

That is very true

freeza36 (author)2011-10-30

Although lines go on forever, they would still be parallel. Both line segments and lines can be parallel.

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