- [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.