Let \(R\) be the relation "is congruent to" on the set of all triangles in a plane. Is R:

\(\text{ Let }S\text{ denote the set of all triangles in a plane.}\\ \text{Let }R\text{ be the relation on }S\text{ defined by }\left({\Delta }_{1},{\Delta }_{2}\right)\in R\\ \Rightarrow \text{ triangle }{\Delta }_{1}≅{\Delta }_{2}.\\ \text{ ( }i\text{ ) Let any triangle }\Delta \in S\text{, we have }\\ \Delta ≅\Delta \\ \Rightarrow (\Delta ,\Delta )\in R\forall \Delta \in S\\ \Rightarrow R\text{ is reflexive on }S\text{. }\)

\(\text{ (ii) Let }{\Delta }_{1},{\Delta }_{2}\in S\text{, such that }\left({\Delta }_{1},{\Delta }_{2}\right)\in R\text{, then }\\ {\Delta }_{1}≅{\Delta }_{2}\\ \Rightarrow {\Delta }_{2}≅{\Delta }_{1}\\ \Rightarrow \left({\Delta }_{2},{\Delta }_{1}\right)\in R\\ \Rightarrow R\text{ is symmetric }\)

\(\text{ (iii) Again, let }{\Delta }_{1},{\Delta }_{2},{\Delta }_{3}\in S\text{ such that }\left({\Delta }_{1},{\Delta }_{2}\right)\in R\text{ and }\\ \left({\Delta }_{2},{\Delta }_{3}\right)\in R\\ ∴{\Delta }_{1}≅{\Delta }_{2}≅{\Delta }_{3}\\ ∴\left({\Delta }_{1},{\Delta }_{3}\right)\in R\\ \Rightarrow R\text{ is transitive. }\)