About this video
Kason rotates triangle ABC about point C and then decides the triangles are not congruent because it doesn't line up with triangle GFE. The video shows he stopped too early: after the rotation, a reflection over line FG maps the triangle exactly onto GFE, so the triangles are congruent.
You'll be able to
- explain that two figures are congruent if a sequence of rigid transformations maps one onto the other.
- combine a rotation and a reflection to map one triangle onto another.
- spot when someone has given up on a mapping too early.
Key words
- congruent
- Two figures are congruent if you can map one exactly onto the other using only rigid transformations.
- rigid transformation
- A move such as a rotation, reflection or translation that keeps lengths and angles the same.
- rotation
- Turning a figure around a fixed point, such as point C.
- reflection
- Flipping a figure over a line so each point lands the same distance on the other side.
- sequence of transformations
- Doing one transformation after another, like a rotation followed by a reflection.
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.
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