R = {(T1, T2) : T1 is congruent to T2}
(i) Since every triangle is congruent to itself
∴ R is reflexive.
(ii) Also (T1, T2) ∈ R ⇒ T1 is congruent to T2 ⇒ T2 is congruent to T1 (T2,T1) ∈ R
(T1,T2) ∈ R ⇒ (T2,T1) ∈ R ⇒ R is symmetric.
(iii) Again (T1, T2), (T2, T3) ∈ R ⇒ T1 i is congruent to T2 and T2 is congruent to T3 ∴ T1 is congruent to T3 ∴ (T1,T3) ∈ R (T1,T2), (T2,T3) ∈ R ⇒ (T1,T3) ∈ R ∴ R is transitive.
From (i), (ii), (iii), it is clear that R is reflexive, symmetric and transitive
∴ R is an equivalence relation.