1. The problem statement, all variables and given/known data For (x, y) and U, v) in R2, define (x,y)~(u,v) if x2+y2 = u2+v2. Prove that ~ defines an equivalence relation on R2 and interpret the equivalence classes geometrically. 2. Relevant equations (none) 3. The attempt at a solution The first part is easy. I proved transitivity, reflexivity, and symmetry as per the definition of an equivalence. I'm a little confused how to do so geometrically. Since x2 + y2 can represent the Pythagorean identity, I'm assuming the proof involves triangles. I understand that the properties of an equivalency (trans, reflect, and sym) can resemble triangle congruence and similarity, but I'm not quite so sure how to apply it. Any hints would be helpful.