Congruent shapes & transformations

Perform a sequence of transformations to try to map the movable figure-- that's this figure right over here-- onto C-O-R-A-L or CORAL. So C-O-R-A-L is this polygon right over here. And then we have to figure out, are these two figures congruent? So they're congruent if, through some combination of translations, rotations, and reflections, I can make this figure sit right on top of figure C-O-R-A-L. So let's use this tool right over here to do that-- to do some translations, rotations, and reflections. And so the first thing I want to do, let me translate it so they get close to each other. And let me see if I can get one point in common. So just like that, I've been able to get this point in common. And it seems like, if these are going to be congruent, that those would correspond to each other. And now it looks pretty clear that these are reflections of each other. So let me reflect them. So it looks like if I were to put my point right there and if I go right in between, it looks like if I reflect right along that, actually, I might end up being done. And I am done. So just with that little translation followed by reflection, I was able to make these two figures sit on top of each other. So these are definitely congruent.