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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??
• 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
• Yes, but the correct spelling is radii (ray·dee·ai).
• i dont think we will need any of this once we grow up
• how do you find out if 2 are similar or congruent on regular pencil and paper?
• 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.
• Would it make a difference if she instead first dilated then translated the circle?
• It doesn't matter. Dilation is not a rigid transformation and will not conserve congruence.
• Is there such thing as a non-rigid transformation?
• 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.
• What are those little apostrophes on top of the letter A’ B’’ C’’’?
• they say at nothing
`:O vrey shock !1!11`