# Similarity and Transformations

## Definitions and step by steps.

Transformation- An operation that maps a geometric figure, preimage, onto new figure,image

Dilation- A transformation that enlarges or reduces a figure by a scale factor

Step 1. Count how many square are in the triangles (doesn't matter which triangle you start with) for example)we'll start with the picture above. From D to E there are 2 squares and from B to C there are 4 squares. From E to F there are 2 squares and fro C to A there are 4 squares. From D to F there are 4 squares and from B to A there are 8 squares.

Step 2. Write ratios comparing the lengths of each side.

DE/BC= 2/4 or 1/2

EF/CA= 2/4 or 1/2

DF/BA= 4/8 or 1/2

Since the ratios are equal, BAC is the dilated image of DFE. So, the two triangles are similar because a translation and a dilation maps DFE onto BAC