# Similarities and Transformation

### Similar and Transformed Figures

## The Different Types of Transformation

There are four types of transformation. The different types of transformations are reflection, rotation, dilation, and translation. Reflection is when a figure is flipped over a line. Rotation is when the figure is rotated by a fixed point. Dilation is when a figure enlarges or reduces by a scale factor. Translation is when a figure slides from one position to another position without any turning. Those are the four types of transformation. A figure can have more than one transformation.

# The Steps to Identify Similar Figures

- When a two figures are similar, it means that the second figure can be obtained from the first by a sequence of transformation and dilation .
- First, you need to determine the transformation used on the figures
- Then, you need to write ratios comparing the lengths of each side
- Reduce the ratios if needed
- If the ratios are the same, then the figures are similar, but if there are different ratios, then the figure isn't similar.

* Something that you should keep in mind is that a figure can have more than one transformation.

Example:

side AB=5 and side DE= 10, and when you reduce the ratio, you get 1/2

side BC=8 and side EF=16, when you reduce the ratio, you get 1/2

side CA=10 and side FD=20, when you reduce the ratio, you get 1/2

~ Since the ratios are all equal, triangle DEF is a dilated image to triangle ABC. So, the two triangles are similar.

# The Steps to Solve Similar Figures but Different Sizes

- You would first need to determine the transformation used
- Then you would write ratios comparing the lengths of each side.
- Reduce down the ratio if needed
- If all of the ratios are the same, then the figures are equal. If the ratios are not equal, then the figures aren't equal.

Example:

The Blue rectangle

width=20 and length=45, when you reduce it down, you get the ratio of 4/9

The Yellow rectangle

width=25 and length=40, when you reduce the ratio down, you get 5/8

~ The ratios are not equal. So, since the ratios aren't equal, the rectangles aren't similar.

# Dealing with Scale Factor

Similar figures have the same shape but different sizes. The sizes of the two figures are related to the scale factor of the dilation. A scale factor is the ratio of the lengths of two corresponding sides of two similar figures.

side AT= 12 and side GD=3, the scale factor for that side is 4

side TC=8 and side DO=2, the scale factor for that side is 4

side CA=16 and side OG=4, the scale factor of that side is 4

~ The scale factor of these two triangles is 4, because when you write the ratios, you get 4 at the end.