Problem #DES-similarity

Problem

It is often the case in geometric situations that figures look very similar, but not quite equal. Two polygons on the plane are called similar if and only if ALL their corresponding angles are equal AND the ratio between ALL the corresponding sides is the same.
The relation between the corresponding sides, in our case it’s $\frac{|AB|}{|IH|}$, is called the similarity coefficient between the figures. It is common practice to write vertices of similar figures in the order that respects the similarity.

We will find some criteria for determining similarity and apply them to solve problems. The statements of some examples and problems may be helpful for problems coming after them!