Let `"T"` be the set of all triangles in a plane with `"R"` as relation in `"T"` given by `R={(T_1,T_2):(\ T)_1~=T_2}` . Show that `"R"` is an equivalence relation.

Explanation

Since a relation `R` in `T` is said to be an equivalence relation if `R` is reflexive, symmetric and transitive.


(i) Since every triangle is congruent itself


`therefore {R}` is reflexive


`(T_{1}, T_{1}) in R Rightarrow T_{1}` is congruent to itself : R Reflexive


(ii) `(T_{1}, T_{2}) in R Rightarrow T_{1}` is congruent to `T_{2}`


`Rightarrow {T}_{2}` is congruent to `{T}_{1}`


`Rightarrow({T}_{2}, T_{1}) in {R}`


Hence R is symmetric


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