Corresponding points and sides of scaled shapes

We are told figure two is a scaled copy of figure one. So this is figure two; here this is figure one. Looks like figure two not only has it been scaled down to a smaller version, but it also looks like it has been rotated 180 degrees, or you could say it's been flipped upside down.

We're asked to identify the side in figure two that corresponds to side EA in figure one. So this is EA in figure one. Pause this video and see if you can identify the side of figure two that corresponds to side EA in figure one.

All right, now let's work through this together. Some of you might immediately intuit or be able to spot which side corresponds to EA, but I'll do it slightly more methodically in this video just so that we can see maybe all of the corresponding sides and points.

One way to think about it is, well, it looks like the longest side in figure one is side BC. So this is the longest side in figure one, and then the longest side in figure two is HL. It looks like BC corresponds to HL.

Then touching on that longest side, that longest side has two right angles. It forms two right angles with the sides next to it. So you have these two right angles right over here. And then of those two right angles, you have the shorter side connected to the longest side, and so that is BA over here. That would correspond to LK right over here; that is the shorter side connected to the long side that forms a right angle.

If we just keep following that side of the shape, we then go to side AE, which would correspond now to—and this is answering our question—to side KJ. So the side in figure two that corresponds to EA in figure one, that is going to be KJ or we could say side JK.

If someone wanted to say what points correspond to which point, well, you can see that BA corresponds to LK and BC corresponds to LH. So we would know, for example, that this point B right over here would correspond to point L in figure two right over here. We could use a similar logic for the other points.

So we've answered the question, but the real thing is to see which sides or points have similar features on a relative basis. I said, what is the longest side? What is the longest side? Where do we see right angles? Sometimes your brain might just immediately be able to spot out the shape. If you were to rotate this one all the way around, it would jump out at you a little bit faster that JK and AE are corresponding sides.