Non-congruent shapes & transformations
About this video
Brenda maps circle M onto circle N using a translation and then a dilation, and claims the circles are congruent. The video explains that a dilation is not a rigid transformation because it changes lengths like the radius, so the circles are not congruent.
You'll be able to
- tell which transformations are rigid and which are not.
- explain why a dilation cannot be used to show two figures are congruent.
- judge whether a congruence claim is correct.
Key words
- translation
- Sliding a figure without turning or resizing it; it is a rigid transformation.
- dilation
- Resizing a figure from a centre point by a scale factor; it changes lengths, so it is not rigid.
- rigid transformation
- A transformation that preserves distances, lengths and angle measures.
- congruent
- Figures that can be mapped onto each other using only rigid transformations.
- radius
- The distance from the centre of a circle to its edge.
Transcript
- [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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