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# Geometric constructions: parallel line

CCSS.Math:

## Video transcript

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 it's going to look like that and then I'm really just going to use the idea of corresponding angle congruence 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 have 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 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 point the distance from those two points and then I can use that up over here to figure out I got a little bit shaky I could figure out that point right over there and just like that I now have two corresponding angles defined by transversal and parallel lines so what I could do this 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