Main content

## High school geometry

### Unit 3: Lesson 8

Constructing lines & angles- Geometric constructions: congruent angles
- Geometric constructions: parallel line
- Geometric constructions: perpendicular bisector
- Geometric constructions: perpendicular line through a point on the line
- Geometric constructions: perpendicular line through a point not on the line
- Geometric constructions: angle bisector
- Justify constructions
- Congruence FAQ

© 2023 Khan AcademyTerms of usePrivacy PolicyCookie Notice

# Geometric constructions: parallel line

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

## Want to join the conversation?

- I'm enjoying these in person videos ;)(8 votes)
- Are there other ways to find out if they are parallel?(2 votes)
- You can use a protractor and measure both angle measures and then check if they are the same which will then show if they are parallel or not(3 votes)

## 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.