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# Similar shapes & transformations

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.