# The angles of similar triangles are equal always, sometimes, or never?

##### 1 Answer

Angles of similar triangles are ALWAYS equal

#### Explanation:

We have to start from a definition of *similarity*.

There are different approaches to this. The most logical one I consider to be the definition based on a concept of *scaling*.

Scaling is a transformation of all points on a plane based on a choice of a *scaling center* (a fixed point) and a *scaling factor* (a real number not equal to zero).

If point

(positive

Then the definition of *similarity* is:

"*two objects are called 'similar' if there exists such a center of scaling and scaling factor that transform one object into an object congruent to another.*"

Next, we have to prove that a straight line is transformed into a straight line parallel to an original.

That causes angles to be transformed into equal angles, which is a subject of this question.

These proofs are presented in the course of advanced mathematics for teenagers at Unizor (follow menu items *Geometry - Similarity*).