Answer to Question #12040 in Discrete Mathematics for Ranjan Chettri
If A is the set of triangles in a plane then prove that the relation R defined by "a is similar to b" is an equivalence relation.
Two geometrical objects (in this case – triangles) are called similar if they both have the same shape, or one has the same shape as the mirror image of the other. Obviously, this relation satisfies following conditions:
a ~ a. (Reflexivity) if a ~ b then b ~ a. (Symmetry) if a ~ b and b ~ c then a ~ c. (Transitivity)