# Similarity and Transformations

## 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