Show that the relation R defined in the set A of all triangles as `R={(T_(1),T_(2)):T_(1)` is similar to `T_(2)`}, is equivalence relation.

Explanation

`R={(T_(1),T_(2)):T_(1)` is similar to `T_(2)`}
R is reflexive since every triangle is similar to itself.
Further, if `(T_(1),T_(2)) in R,` then `T_(1)` is similar to `T_(2)`.
`implies T_(2)` is similar to `T_(2)`
`implies (T_(2),T_(1)) in R`.
Therefore, R is symmetric.
Now, let `(T_(1),T_(2)),(T_(2),T_(3)) in R`.
`implies T_(1)` is similar to `T_(2)` and `T_(2)` is similar to `T_(3)`
`implies T_(1)` is similar to `T_(3)`
`implies (T_(1), T_(3)) in R`
Therefore, R is transitive.
Thus, R is an equivalence relation.