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  • - [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.

- [Instructor] We are told, Brenda was able to map

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