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

Similar triangles & slope: proportion of segments | Grade 8 (TX) | Khan Academy


2m read
·Nov 10, 2024

We're told triangle PQR and triangle ABC are similar triangles. Which proportion shows that the slope of PR, right over here, equals the slope of AC?

So pause this video and see if you can figure that on your own before we do this together.

All right, well, let's just think about how we can express each of these slopes in terms of the other sides of this triangle. We know that slope is change in y, so slope is change in y over change in x. If we were to say to go from point A, right over here, to point C, what is our change in y? Well, our change in y is the length of this line right over here. So our change in y is going to be the length of segment AB, which we could just write as AB.

And then our change in x is going to be the length of segment BC. That's our change in x. So it's AB over BC. Now, let's do the same thing for this triangle right over here. I'll do it a different color. What's our change in y? Well, our change in y is the length of segment PQ.

So let me write this: change in y over change in x. Our change in y is the length of segment PQ. When we don't write the little line segment on top, this means we're talking about its length and not the segment itself. And now what's its change? So this is its change in y.

And then the change in x, going from P to R, change in x is segment QR, the length of segment QR. And so we also know that these slopes are going to be the same because the slope of a line is constant everywhere. We also know that because these are similar triangles, if you take the ratio of the corresponding sides, you're going to have the same ratio.

So what we know is that this slope right over here needs to be equal to this slope right over here. Or we could say AB over BC should be equal to PQ over QR.

Now, which of these says that? So this one has PQ over QR and it has AB over AC, not BC, so I'll rule that one out. This one has PQ over QR; it has AB over BC. I'm liking this one.

Let's see. This one has QR over PQ; that's not the slope of this one over here, and so I'm not going to like that one. And this one also says QR over PQ and has AB over AC, so I don't like that one either.

So we're done. It's this choice B.

More Articles

View All
Names
Hey, Vsauce. My name is Michael. And my name is Kevin. Names. Humans give each other names, but so do dolphins. They use whistle sounds and will respond to their whistle name even when produced by a dolphin they don’t know. Personal names, personalized t…
Hunting for Emeralds | Mine Hunters
Next morning, the teams start early on their first day’s work at Player Verie. “Oh look, here’s all the Timbers!” First up, Fred and Zach do an inventory of equipment at the site. “Hey, what’s this? It’s a blower! We can use this to ventilate the mine, …
The world's first medical delivery drone. ⛑️
My name is Tom. I’m one of the founders of WinCopter, a drone delivery company. We manufacture, but also we deploy and service delivery drones. So, we build drone logistic networks across countries; later on, hopefully, continent. We really laser focus o…
Adorable Bear Cubs Crash Campsite | Expedition Raw
So I just came around the corner, found this female on the beach here, and I thought I recognized her. She’s one of the mothers as having cubs. So I was looking for the cubs all up in the forest here, and then all of a sudden I was like, “Ah, there they a…
Kevin O'Leary: Harvard's Most Controversial Case Study?
At Harvard, why this is Kevin O’Leary building a brand in shark-infested waters? It’s a Harvard case about Mr. Wonderful. I can’t believe it; it’s surreal. Of course, I’m honored, no question about it. The whole story is in here, the whole Mr. Wonderful s…
15 Things That Seem Important But Aren't
You know, from the moment we wake up in the morning, we can feel society’s pressures looming over us like a dark cloud, can’t we? But what if some of the things they tell us we need to have aren’t really that important at all? What if we could kick these …