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Geometric constructions: parallel line

We can parallel lines with compass and straightedge by creating a pair of congruent corresponding angles on a transversal.

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  • sneak peak blue style avatar for user padams
    I'm enjoying these in person videos ;)
    (25 votes)
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  • piceratops ultimate style avatar for user Woohoo
    Are there other ways to find out if they are parallel?
    (4 votes)
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  • primosaur ultimate style avatar for user Thiam
    i have a better idea
    1. place the needle end of the compass on the point and make the distance a bit further than the line, then draw an arc so that there are 2 intersecting points on that line
    2. let those two intersections be your line segment and bisect it
    3. draw a circle with the compass needle at the original point, let those intersections be your new segment
    4. bisect that segment

    if you need any further elaboration let me know, im better with showing people rather than telling
    (7 votes)
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  • piceratops ultimate style avatar for user Bot
    Why does it say [David] in the subtitles at the beginning of the video?
    (3 votes)
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    • female robot grace style avatar for user Cynthia
      Hello @Bot,

      Subtitles often have to be a paraphrase of what is actually said in order to make it possible to read them at the same speed as the spoken dialogue. It conveniently bridges the language gap of global audiences while preserving the original audio performances. Subtitles are a form of captioning used to translate the audio dialogue from one language into another. Simply put, subtitles translate a video's language into another. You'll see subtitles used in many foreign films and programs. On the other hand, Closed Captions are in the same language as the original audio.

      (1 vote)
  • duskpin tree style avatar for user Steph
    I have tried to do this 5 times on a piece of paper and not once have i gotten parallel lines. PLEASE HELP!
    (2 votes)
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  • starky ultimate style avatar for user 🐱‍👤 CodeNinja 🐱‍👤
    This video represents a angle-side-angle congruence
    (0 votes)
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Video transcript

- [David] Let's say that we have a line, drawing it right over there, and our goal is to construct another line that is parallel to this line that goes through this point. How would we do that? Well, the way that we can approach it is by creating what will eventually be a transversal between the two parallel lines. So let me draw that. So I'm just drawing a line that goes through my point and intersects my original line. Do that, so it's going to look like that. And then, I'm really just going to use the idea of corresponding angled congruents for parallel lines. So what I can do is now take my compass and think about this angle right over here. So I'll draw it like that. And say, all right, if I draw an arc of the same radius over here, can I reconstruct that angle? And so where should the point be on this left end? Well, to do that, I can just measure the distance between these two points using my compass, so I'm adjusting it a little bit to get the distance between those two points. And then I can use that up over here to figure out, I got a little bit shaky. I can figure out that point right over there. And just like that, I now have two corresponding angles to find my transversal and parallel lines, so what I can do is take my straightedge and make it go through those points that I just created, so let's see, make sure I'm going through, and it would look like that, and I have just constructed two parallel lines. And once again, how do I know that this line is parallel to this line? Because we have a transversal that intersects both of them and these two angles, which are corresponding angles, are congruent. So these two lines must be parallel.