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Congruent shapes and transformations

less than 1m read
·Nov 10, 2024

We're told Cassandra 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.

Then they say Kasan 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 Kasan correct that they are not congruent because you cannot map 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, there's rotation about point C. And so, this point right over here, let me make sure I get this right, this would have 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, Kasan is not correct; he missed one more transformation he could have done, which is a reflection.

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