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## High school geometry

### Course: High school geometry>Unit 3

Lesson 1: Transformations & congruence

# 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).
• 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.
• is there other basic rigid motions other than reflect,translate, and rotate?

as said in
• Those three translations are the three basic geometric translations besides dilation.
• they say at nothing
• When reflecting a figure in a plane, do the images have to be exactly the same size as their preimages? Cant they be a few centimeters bigger or smaller?
• If the images weren't the same size as their preimages, they would not be part of the same transformation. When you reflect a figure across a axis, the on ly thing changing is the orientation of the figure, not the size or shape.
• 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.
• What is exactly a translation and a dilation?
• EDIT

I messed up with my explanation of dilation here, so look at my next response in comments. Thanks to david severin for pointing it out.

translation is moving up, down, left, right or a combination, then a dilation is more complicated

Dilation is basically stretching or compressing, so making a graph wider, or longer or skinner or something. for example, tae the simple x^2. if you had 4x^2 the graph would be stretched upward by a factor of 4, so it would get skinnier. if instead it was (2x)^2 this is a horizontal compress by a factor of 2. It's worth noting these two are the same, so a vertical stretch is a horizontal compress and vice versa.

What do they mean? well a vertical stretch means the point (2,4) will increase vertically by quadrupling the y value, so it turens to (2,16). so the y vlue is multiplied. a compress divides the coordinates. so horizontal compress would cut the x value in half so (2,4) would become (1,4)

Let me know if this doesn't make sense.