Non-congruent shapes & transformations

2m read

·Nov 10, 2024

[Instructor] We are told, Brenda was able to map circle M onto circle N using a translation and a dilation. This is circle M right over here. Here's the center of it. This is circle M, this circle right over here. It looks like at first, she translates it. The center goes from this point to this point here. After the translation, we have the circle right over here. Then she dilates it. The center of dilation looks like it is point N. She dilates it with some type of a scale factor in order to map it exactly onto N. That all seems right.

Brenda concluded, "I was able to map circle M onto circle N using a sequence of rigid transformations, so the figures are congruent." Is she correct? Pause this video and think about that. Let's work on this together. She was able to map circle M onto circle N using a sequence of transformations. She did a translation and then a dilation.

Those are all transformations, but they are not all rigid transformations. I'll put a question mark right over there. A translation is a rigid transformation. Remember, rigid transformations are ones that preserve distances, preserve angle measures, preserve lengths, while a dilation is not a rigid transformation.

As you can see very clearly, it is not preserving lengths. It is not, for example, preserving the radius of the circle. In order for two figures to be congruent, the mapping has to be only with rigid transformations. Because she used a dilation, in fact, you have to use a dilation if you wanna be able to map M onto N because they have different radii, then she's not correct. These are not congruent figures. She cannot make this conclusion.

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Non-congruent shapes & transformations

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