# Similarity and Transformations

### WHAT IS IT AND HOW DO YOU FIGURE IT OUT?

## What is similarity?

Similarity is when 2 or more figures have the same sides, shape, or appearance.

But that's always the case. Two figures can be similar if the second can be obtained by a number of transformations and dilation.Here is a simple picture of classification. you can easily classify then by their shape, size, and color.But can you classify them by their angles and vertices and more?

## Translation Moving a shape, without rotating or flipping it. You bascially are just sliding over the plane. | ## Reflection Reflection means when the figure is the mirror image of the other on a coordinate plane. Here is the a to the left. | ## Dilation Dilation means to increase in size from its original shape size. |

## Translation

Moving a shape, without rotating or flipping it. You bascially are just sliding over the plane.

## Reflection

Reflection means when the figure is the mirror image of the other on a coordinate plane. Here is the a to the left.

## " Step 1 "

Using the picture below since the image stayed the same but only grew larger( basically the orientation stayed the same). first identify the transformations present in the picture. The only transformation present is a dilation so to figure out the difference all they did was move ^ABC 1 unit up then 2 1/2 units right. So A=A' is now (2,6) and so on.

## Step 2

Using the same image you are now going to create ratios to compare the lengths of the sides for the image. so..

AB = 2 1. AC = 3

------ ~or ~ ------ ~ but this pair isn't equal so it doesn't count. (AC=A'C')

A'B'= 4 2. A'C'= 5 .

There is no need to do CB and C'B' because its equal to AB A'B'C'. So now knowing that you know the 2 images are similar because a dilation maps ^ABC to ^A'B'C' . So that's how you figure out similarity by using transformations. Hope you learned something new :)