Definition of similar rectilinear figures (Euclid's Elements) Definition 6.1 of Euclid's _Elements_ states: > Similar rectilinear figures are such as have their angles severally equal and the sides about the equal angles proportional. I wonder if the 'equal angles' part is necessary. In other words, is it possible for two rectilinear figures to have their respective sides proportional but the respective angles unequal?

The 'equal angles' part is not necessary to be stated for triangles since specifying the $3$ triangle side lengths uniquely identifies their internal angles. However, it's needed for figures with $4$ or more sides to be considered similar. For example, there are parallelograms (without right angle corners) and rectangles with equal corresponding side lengths that are not similar to each other.