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Sal is given pairs of polygons, and then he determines whether they are similar by trying to map one onto the other using angle-preserving transformations. Created by Sal Khan.
Video transcript
These two quadrilaterals, EFGH and ABCD, these are similar. If through some combination of translations, rotations, reflections, and dilations, I can make them sit on top of each other. And similarity allows us to use dilations, which essentially means scale up one of the figures up or down. If we're talking about congruence, then we wouldn't be scaling the figures up or down. We would only be translating, rotating, and reflecting. But let's see if we can do it. So let's first translate it. Let's first translate this figure. So let's make that point on top of that point. And now let's rotate it. I'm going to rotate it around point E right over here. So I get right over there. So I got two of the sides to kind of match up. But now let me dilate it down. Let me scale it down. And so this is-- let me put it on what I want to not change-- and then let me see if I can scale this down. And I was able to. So through just purely translations, rotations-- I didn't even have to use the reflections-- translations, rotations, and dilations, I was able to make these sit on top of each other. So these two figures are similar. So yes, the rectangles are similar. Let's do one more of these. So these two triangles-- and just eyeballing it, this one looks kind of taller than this one does right over here. So they don't feel similar, but let me at least try. So let me translate, maybe make this point C might correspond to point F, although it already looks pretty clear that it won't. But now let me dilate it. So I'll keep that point where it is. And let me try to scale this up. And then we see pretty clearly we made segment CB sit on top of, after scaling it up, sit on top of segment FE. But then everything else is not matching up. Point D is in a very different place than where point A is once I try to scale things up a little bit. So these two triangles are clearly, clearly not similar.