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
This Video Will Make You Angry
Hello Internet. Thoughts compete for space in your brain: cat photos, news stories, belief structures, funny GIFs, educational videos, not-so-educational videos, and your thinking inventory is limited. A thought without a brain to think it dies. Now we ca…
6 things you probably need to hear
Here are six things you probably need to hear. Number one: Nobody is on their way. This is something that everybody has to realize at some point in their life, and some people realize it when it’s far too late. And that is that nobody is on their way to …
Interpreting motion data | Physics | Khan Academy
Let’s learn about position time graphs and position time tables to analyze motion. Let’s start by considering a car going at a constant velocity. To create a position timetable, let’s take snapshots of it at, say, every five seconds. So here we go, boom! …
Introduction to proteins and amino acids | High school biology | Khan Academy
What we’re going to do in this video is talk about proteins. Some of you all might already be familiar with them, at least in some context. If you look at any type of packaging on food, you’ll oftentimes see a label that has protein listed in a certain nu…
The Firefighting-inspired Watch #shorts #watch
I should disclose right now then, so we actually make the watches, Kevin, from genuine upcycled firefighting materials. Even elements of the case, which you can see by the striking strap that you have on your wrist. Yes, I should disclose right now that I…
$26k Cash Grant For Your Business? Mr. Wonderful on Tucker Carlson Today
Kevin O’Leary is one of the most successful, certainly one of the most famous investors and businessmen around. Because he’s a TV star in addition to a businessman, he’s on Shark Tank and has been for 15 years. We talked to him for a brand new episode of …