The Petersen-Schoute theorem is a beautiful general theorem of which the following two statements are special cases (Coxeter and Greitzer 1967, pp. 99-100).
1. If 
and 
are two directly similar triangles, while 
,
,
and 
are three directly similar triangles, then 
is directly similar to 
.
2. When all the points 
on 
are related by a similarity
transformation to all the points 
on 
, the points dividing the segment 
in a given ratio are distinct and collinear,
or else they coincide.
