Question

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?

Answer 1

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.

The relation R shows a relation of linear sizes (legs) of similar triangles.

$$A(a) = R * A(b), \ B(a) = R * B(b), \ C(a) = R * C(b)$$