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## High school geometry

### Course: High school geometry>Unit 4

Lesson 1: Definitions of similarity

# Similar shapes & transformations

Two shapes are similar if we can change one shape into the other using rigid transformations (like moving or rotating) and dilations (making it bigger or smaller). Other kinds of transformations can change the angles or the ratios of lengths in a figure. If we need those types of transformations, the shapes are not similar. Created by Sal Khan.

## Want to join the conversation?

• Is there a video where Sal formally defines "Dilation"? • I practiced the concept and it is totally different on what you have to do... help? • This video is fairly old, the exercise has probably been updated since the video was recorded. However, I'm sure it shouldn't be too different.
1 minute later after Ayaka has rewatched the video and looked at the exercise
It is that much different x.x
-Translation: Instead of dragging a shape around, it requires you to enter in how much you want to move it by. Remember, x comes first, y second. So putting in (-5, 6) would move it 5 to the left and 6 up.
-Rotation: Rather than dragging the arrow around, it wants you to put in where you're rotating it about. Best to enter in the coordinates of one of the points of your shape, preferably the one that overlaps a point of the other shape. Then put in how many degrees you want to rotate your shape by. There are 360 degrees in a circle, so entering in 360 will bring it all the way round. 180 will effectively flip it over and 90 will bring it round by a quarter, or half of a half.
-Reflection: Reflection baffled even me at first glance. It is extremely hard to use! Imagine a line segment coming from the first set of coordinates you give, ending at the second set. The shape you have will flip over that line.
-Dilation: The coordinates are the coordinates of where you would have put the center of the original circle dilation tool. The third number you put in is how much to dilate by. If you say 2, the shape will be 2 times as big. If you say 0.5, the shape will be 0.5 times as big.
-Rage quitting: Don't.
• What is an example of a transformation that is not a similarity transformation? • So two figures are congruent if you can map them onto each other using a series of rigid transformations so that corresponding parts are equal to each other, and two figures are similar if you can map them onto each other using rigid transformations and a dilation. Sal mentions that all congruent shapes are similar, but aren't congruent shapes limited to rigid transformations? How is this possible? Please correct me If I'm missing something, thanks! • Hi RN,
I think that what Sal meant was all congruent shapes are similar but not all similar shapes are congruent if that isn't too confusing.
For instance, you can map 2 congruent triangles onto each other with rigid transformations and technically, that would make it similar too, but you couldn't map 2 similar triangles onto each other without using a non-rigid transformation which would mean the triangles aren't congruent.
I think a shape doesn't have to be dilated in order to be similar but all dilations cause shapes that are similar.
I hope this helps!
(Let me know if it doesn't or if I'm wrong.)
• So i guess a vertical stretch wouldn't preserve anything, right?

Or is that the same as dilation? it seems as though if sal or "shui" could use a vertical stretch in the problem, but does that not keep similarity?

thanks :) • Vertical stretch occurs when a base graph is multiplied by a certain factor that is greater than 1. This results in the graph being pulled outward but retaining the input values (or x). When a function is vertically stretched, we expect its graph’s y values to be farther from the x-axis.
I don't think this will help, but it might.
Calc-Ya-Later!
• I am doing a problem that asks me to determine which of two people are correct in solving a problem. The possible solutions that I have to choose from are transformation and glide-reflection. I understand what transformation is and that it is most likely the correct answer, but what is glide-reflection? I have never heard of it, and I need to explain why this would not be the correct way to solve the problem. Is there a video where Sal explains glide-reflections? Thanks! • Couldn't find anything on the web about there being a fifth transformation, but the answer to this problem speaks as if there are more transformations past dilation,(-) so does anyone know if there are more non-rigid transformations besides dilation or not? Or do they just mean that a rotation or reflection would have to go either replace and/or go into play? • The one you're thinking of might be glide reflection, which is a translation followed by a reflection across that line of translation. But there are no other transformations of this type. Every similarity can be written as a single dilation, followed by a single reflection, translation, glide reflection, or rotation.
• Okay, so the shapes have to have the exact same side sizes to be congruent, right?

I was doing some of the exercises on congruency and similarity yesterday, but I kept on getting the answer wrong, and then I changed and it still didn't like me. I think you might need to change them or something.   