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### Course: Basic geometry and measurement > Unit 14

Lesson 7: Congruence and similarity# Non-congruent shapes & transformations

Congruent shapes are the same size and shape. Rigid transformations, like translations, keep shapes congruent, but dilations are not rigid transformations because they change the size. So, if we use a dilation to map one shape onto another, they are not congruent. Created by Sal Khan.

## Want to join the conversation?

- When I take the test (at school) on this topic, we're not going to have the tools that you have when you showed us. So my question is, how do you know if the two shapes are congruent without using the tools?

In other words, is there a way to use the graph coordinates to figure out if the two shapes are congruent or not??(19 votes)- i think even though this comment was a while ago you can take the dimensions of one and the dimensions of the other and see if they are the exact same(10 votes)

- Is radi plural for radius?(4 votes)
- Yes, but the correct spelling is radii (ray·dee·ai).(6 votes)

- how do you find out if 2 are similar or congruent on regular pencil and paper?(4 votes)
- You can use distance formula to prove that the sides are congruent, and that if the sides are congruent, then the shapes are congruent, but that takes a long time and is annoying. Later you will learn a bunch of postulates that prove congruence.(5 votes)

- Would it make a difference if she instead first dilated then translated the circle?(2 votes)
- It doesn't matter. Dilation is not a rigid transformation and will not conserve congruence.(7 votes)

- Two objects are congruent if they are the same size and shape. We can also define objects as congruent if we can move one object to obtain the other object through a congruence transformation. A congruence transformation is a transformation that doesn't change the size or shape of an object.(5 votes)
- Is there such thing as a non-rigid transformation?(3 votes)
- Yes, most transformations of the plane are non-rigid. The transformation which maps each point (x, y) to (x²+y², xy) is non-rigid, since it doesn't map straight lines to straight lines.(4 votes)

- What are those little apostrophes on top of the letter A’ B’’ C’’’?(4 votes)
- Prime. It's supposed to represent the new points after the transformation. It's pronounced "A-prime" or "B-prime" (or in your case "B-prime-prime")(1 vote)

- they say at2:03nothing(3 votes)
- i did the same question on the next practice(3 votes)
- This link could give you a variety of questions if you keep doing the problems.

https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/congruent-similar/e/exploring-rigid-transformations-and-congruence

Hope this helps!

- Sam(3 votes)

- This makes no sence

]\(3 votes)

## Video 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.