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# Similarity & Transformations

## Finding Similarities

To find out the similarities in two or more figures, you would have to figure out the sequence of transformations and dilations.

There are four types of transformations:

Translations- is a transformation used to slide a figure from place to another.  Reflection- is a transformation where a figure is flipped over a line.                Rotation- is a transformation used to turn a figure in a certain direction.      Dilation- is a transformation where a figure is enlarged or reduced into a new figure.

The first thing you do to find the similarity, is to see if the figures' orientations are the same.Then, if they are you would see which transformation has been used. If the figure was translated, determine how many units the figure has been translated to. After that, see if the figure maps onto the other figure. Write ratios comparing the lengths of each side.

Example #1:

ED/HG = 4/8 or 1/2,  DF/GI = 3/6 or 1/2, FE/IH = 5/10 or 1/2

If the ratios are equal, then figure 1 is the dilated image of figure 2.

Example #2:

WT/XY = 5/7, UV/ZW = 5/7, TU/YZ =3/4, VW/WX = 3/4

If the ratios don't equal, then figure 1 can't be the dilated image of figure 2.

This is an example of the transformation reflection.