# Similarity and Transformations

### Tiara Goodwin

## Finding out if two triangles are similar

__Step 1 ~ __ Translate triangle ABC , 5 units left and 3 units up.

*Step 2 ~ * Compare the two triangles using ratios, to see if they are similar.

AB/AB' = 5/5 or 1 BC/BC' = 1.5/1.5 = 1 AC/AC' = 3/3 =1

__Formula~__ Side of original figure / Side of translated figure = How many units are on that side of the original figure / How many units are on that side of the new figure

Since all of the ratios are the equal, after the translation of triangle ABC to ABC' they are similar.

__Step 1~__** ** Fist dilate triangle CDAG by 2 . Then translate rectangle CDFG 1 unit down and 5 units right.

__Step 2~__** **Write ratios comparing the two rectangles to see if they are similar.

*CD/CH= 4/8 or 1/2 DA/HG= 2/4 or 1/2 AG/GF=4/8 or 1/2 GF/FC=2/4 or 1/2*

*Since all of the ratios are equal rectangle CDAG and rectangle CDFG are congruent or similar. *

*similar ~*if one image can be obtained from another by a sequence of transformations and dilations*Transformations ~*an operation that maps a geometric figure, preimage, onto a new figure , image.*Translations ~*a transformation that slides a figure from one position to another without turning