yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Geometric constructions: parallel line | Congruence | High school geometry | Khan Academy


2m read
·Nov 10, 2024

Let's say that we have a line. I'm 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, doing that. So 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 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 between those two points, and then I can use that up over here to figure out—and 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 is take my straight edge and make it go through those points that I just created. So let's see, make sure I'm going through them, 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.

More Articles

View All
Mr. Freeman, part 24
… Not bad … But I did not say that money is a bad thing. I respect every religion … as servile, as it is. Oh … yes … you do not know … Only calm down, stop splashing with your spinal cord. MONEY IS GOD. And you believe religion is Christianity, Buddhism,…
Principles for Success: “The Five Step Process” | Episode 3
[Ray] Principles for Success: An Ultra Mini-Series Adventure in 30 minutes and in eight episodes. Episode three: The Five-Step Process. We’ve discussed how important it is to reflect carefully after experiencing pain. When I did this, I was usually able…
✈️ The Maddening Mess of Airport Codes! ✈️
There are thousands of airports connecting cities across countries and continents. Yet, with just three letters from AAC and BBI to YYZ and ZZU, both me and you and our bags root round the world as unambiguously as practically possible: airport codes. If…
Khan Academy Ed Talk with Bob Hughes - Tuesday, March 23
Hi everyone, Sal Khan here from Khan Academy. Welcome to our Ed Talks live stream, which you could view as a flavor of our Homeroom live stream. Uh, and before we jump into a very exciting conversation with Bob Hughes, who’s the Director of K-12 U.S. Educ…
360° Climbing Giants | National Geographic
[Music] [Music] My name is Wendy Baxter, and I have probably one of the coolest jobs on the planet. [Music] I get to climb in and study giant sequoia trees. My name is Anthony Ambrose, and I am a canopy biologist. I’ve loved trees and climbing trees my en…
Great Schism or East-West Schism part 2 | World History | Khan Academy
Now, the notion of the Holy Roman Emperor and the Holy Roman Empire does not last much beyond Charlemagne. After his death, over the course of the 9th century, his empire is broken up. His successors are not able to carry on the title. But then we get in…