Let be $abc$ and $a'b'c'$ two triangles with same angles, so $ \alpha= \alpha ', \beta= \beta', \gamma= \gamma ' $
I want to show that the triangles are similar to each other by describing a similarity transformation (a translation and scaling) which maps $abc$ onto $a'b'c'$.
I am not sure how to describe that transformation .. my idea is first rotating triangle by a factor $ \mu$ $ abc$ $$A= \begin{pmatrix} 1 & 0 \\\ 0 & \mu \end{pmatrix} $$ How do I proceed with the scalling? Do I understand it right: Two triangles are similar if you can express one triangle as a concatenation of a translation and scalling of the other?
Any help appreciated