Which rigid transformation S can map Triangleabc onto Triangledec?

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Which rigid transformation(s) can map TriangleABC onto TriangleDEC?

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Which rigid transformation S can map Triangleabc onto Triangledec?

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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.

Which rigid transformation S can map Triangleabc onto Trianglefed?

Which rigid transformation(s) can map ABC onto FED? The triangles are congruent by the SSS congruence theorem.

Which rigid transformation S can map Triangleabc onto Trianglefed the triangles are congruent by the SSS congruence theorem?

rotation, then translation, then reflection. The triangles are congruent by the SSS congruence theorem. Which rigid transformations(a) can map triangle ABC onto triangle FED?

Which rigid transformation can be map ABC onto DEC?

triangle DEC under the same line reflection, then ABC ≅ DEC because a line reflection is a rigid motion and triangles are congruent when one can be mapped onto the other using a sequence of rigid motions.

What are the rigid transformations that will map?

Reflections, translations, rotations, and combinations of these three transformations are "rigid transformations".