SOLUTION: Let P be the set of all triangles in a plane and R be the relation defined on P as aRb if a is similar to b. Prove that R is an equivalence relation.

1)  each triangle is similar to itself.


    (The proof is obvious).



2)  if triangle "a" is similar to triangle "b", then the triangle "b" is similar to triangle "a"  

    (the reflexive property of equivalence, or symmetry property).


    The proof is OBVIOUS, again. All you need to know is the definition of the triangles similarity.



3)  If triangle "a" is similar to triangle "b"  and  triangle "b" is similar to triangle "c",  

    then triangle "a" is similar to triangle "c" (transitivity property of equivalence).


    The proof is OBVIOUS, again. Use the definition of the triangles similarity.