Identifying scaled copies

What we're going to do in this video is look at pairs of figures and see if they are scaled copies of each other.

So for example, in this diagram, is figure B a scaled version of figure A? Pause the video and see if you can figure that out.

There are multiple ways that you could approach this. One way is to say, well, let's see what the scaling factor would be. So we could look at this length side length. This side right over here has length 3 on figure A. This side length right over here has length one, two, three, four, five. This side length has length five as well. This has length five.

We could figure it out with the Pythagorean theorem, but I won't even look at that one just yet. But let's look at corresponding sides. So to go from this side, if we scale up, the corresponding side to that would be this side right over here. And what is its length? Well, its length when you scale it up looks like five.

So to go from three to five, you would have to multiply by five thirds. But let's look at this side now. So it's five in figure A. What length is it in figure B? Well, it is one, two, three, four, five. It's still five. So to go from five to five, you have to multiply by 1.

And so you have a different scaling factor for corresponding, or what could have been corresponding sides. This side right over here, you're scaling up by five thirds, while this bottom side, this base right here, you're not scaling at all. So these actually are not scaled versions of each other.

Let's do another example. So in this example, is figure B a scaled version of figure A? Pause the video and see if you can figure it out.

All right, well, we're going to do the same exercise, and here they've given us the measures of the different sides. So this side has length 2. This side has length, the corresponding side, or what could be the corresponding side, has length 6. To go from two to six, you have to multiply by three.

If we look at these two potentially corresponding sides, that side and that side, once again, to go from four to twelve, you would multiply by three. So that is looking good as well. Now, to go from this side down here, this has length six. The potentially corresponding side right over here has length 14.

Well, here we're not multiplying by 3. If these were scaled, if figure B was a scaled-up version of figure A, we would multiply by 3. But 6 times 3 is not 14; it's 18. So these actually are not—figure B is not a scaled version of figure A.

Let's do one more example. So once again, pause this video and see if figure B is a scaled version of figure A.

So we're going to do the same exercise. Let's look at potentially corresponding sides. So that side to that side— to go from 4 to 12, we would multiply by 3. Then we could look at this side and this side. To go from 4 to 12, once again, you multiply by 3.

So that's looking good so far. We could look at this side and this side—potentially corresponding sides. Once again, we're going from 4 to 12, multiplying by 3 looks good so far. And then we could look at this side and this side—2.2 to 6.6, once again multiplying by 3, looking really good.

And then we only have one last one to check—2.2 to 6.6, once again multiplying by 3. So all of the side lengths have been scaled up by 3, so we can feel pretty good that figure B is indeed a scaled-up representation of figure A.