Geometry Geometry

Congruent Figures



Who’s got a theory for which shapes get circled?

Thanks to Professor Danielson for the submission.

4 replies on “Congruent Figures”

This is one of those concepts we teach and practice, but seldom seems to have transfer for students. When do they need to know this is their daily lives? It’s a word they only use in math class.

I believe that this exercise pertains also to Spatial Reasoning which is very important.

My conjecture:
The directions (and problems #1 and #2) prime the student to believe that there must be at least one shape that isn’t congruent. Since a lot of our world is symmetric left/right (faces, animals, etc.), our brains can easily see 3 b) as being congruent to the original. 3 a) looks longer so it doesn’t look congruent. 3 c) looks like 3 a) so it isn’t too. I doubt the student spent a lot of time on it since it is the last problem and they had better things to do. 🙂

Playing Tetris for many hours might actually help the student in this area. 🙂

I’ll weigh in here, briefly. This is my son Griffin’s work. We talked about his choices after I took this photo. I was surprised that he got both of the figures in #1, but missed some in #3. And I would have expected him to get the last choice in #3 before the second one, since you have to flip to get the second one, whereas you only have to rotate to get the third one—the latter being a mental manipulation that is easier for most people.

Something about the rectilinear nature of #3 seemed to trigger a different way of thinking for him. We ended up cutting out the original figure, and he used that to check whether the others were the same. This seemed to be helpful. I’ll have to revisit sometime soon and see whether he’s got it now.

I gladly accept your Tetris prescription, David.

Christopher, is it possible that the optical illusion quality of the choices in #3 threw Griffin off? I had to do a double-take myself because, at first glance, the two options that are not circled appear to be wider (greater area) than the original shape.

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