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Congruent shapes & transformations

If we can map one figure onto another using rigid transformations, they are congruent. They are still congruent if we need to use more than one transformation to map it. They aren't if we use a transformation that changes the size of the shape. Created by Sal Khan.

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Video transcript

- [Instructor] We're told, "Kason was curious "if triangle ABC and triangle GFE were congruent, "so he tried to map one figure onto the other "using a rotation." So let's see, this is triangle ABC, and it looks like, at first, he rotates triangle ABC about point C, to get it right over here, so that's what they're depicting in this diagram. And then they say, "Kason concluded: "It is not possible to map triangle ABC "onto triangle GFE using a sequence "of rigid transformations, "so the triangles are not congruent." So what I want you to do is pause this video and think about, is Kason correct that they are not congruent, because you can not map ABC, triangle ABC onto triangle GFE with rigid transformations? All right, so the way I think about it, he was able to do the rotation that got us right over here, so it is rotation about point C, and so this point right over here, let me make sure I get this right, this would've become B prime, and then this is A prime, and then C is mapped to itself, so C is equal to C prime. But he's not done, there's another rigid transformation he could do, and that would be a reflection about the line FG. So if he reflects about the line FG, then this point is going to be mapped to point E, just like that. And then if you did that, you would see that there is a series of rigid transformations that maps triangle ABC onto triangle GFE. So Kason is not correct, he missed one more transformation he could've done, which is a reflection.