Two triangles are similar if all the corresponding angles are equal.
Then the ratios of the corresponding sides to each other are the same for both triangles.
In the fig above AB/BC = DE/EF or AB/DE = BC/EF.
A list of all the cases of similarity:
Fractals are made up of similar geomtetrical objects.
See e.g. the Serpinski triangle.
Fracrtals can be used to describe objects encounterd in real life such as coastlines, trees or clouds.