Perpendicular lines create a similar triangle? 
In my physics book, it says that since both $V_1$ and $V_2$ are perpendicular to the lines joining them to the center of the circle (the blue radius lines), this means that the blue lined triangle (when joined) is a similar triangle to ($V_1 + \Delta V)$, thus making the angle between $V_2,  V_1$ being $\theta$.
This is confusing for me, because when searching the internet, it says that there are only two means of a triangle being similar to another, SSS, SAS, and AAA.  This text does not meet any of the rules.  What am I missing?
 A: The angle beween $V_1$ and $V_2$ is $\theta$ because $V_2$ is obtained by a rotation of $V_1$ by $\theta$, as you can check by translating them to the origin ($V_1$ forms an angle $\pi/2$ with the $X$-axis, while $V_2$ $\pi/2+\theta$). If you want to translate this in a language of similiar triangels you can, but personally I see it more clearly by thinking about rotations. 
A: Regarding the similarity between the triangles, the previous answer shows us that the blue triangle formed with the two sides of lenght $r$ and the third one $\Delta r$ [Note : it is not the space travelled on the circular path, but the vector "displacement"], and the other triangle formed by the vectors $V_1$, $V_2$ and $\Delta V$ are similar.
This is so because $|V_1| = |V_2| = r ∗ \omega$, thus :

$$\frac{|V_1|}{|r|}=\frac{|V_2|}{|r|}$$

and the angle formed by $V_1$ and $V_2$ is equal to $\theta$.
Thus we apply the SAS criteria for silmilarity (Side-Angle-Side) and conclude with similarity.
Having shown this, we have that also the third couple of sides must be proportional, i.e. :

$$\frac{|\Delta V|}{|\Delta r|} = \frac{|V_1|}{|r|}=\frac{|V_2|}{|r|}$$

Thus also $|\Delta V|$ and $|\Delta r|$ are proportional with ratio $\omega$ .
