(A) reflexive but not transitive

(B) transitive but not symmetric

(C) equivalence

(D) none of these

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- A relation R in a set A is called $\mathbf{ reflexive},$ if $(a,a) \in R\;$ for every $\; a\in\;A$
- A relation R in a set A is called $\mathbf{symmetric}$, if $(a_1,a_2) \in R\;\Rightarrow\; (a_2,a_1)\in R \; for \;a_1,a_2 \in A$
- A relation R in a set A is called $\mathbf{transitive},$ if $(a_1,a_2) \in R$ and $(a_2,a_3) \in R \; \Rightarrow \;(a_1,a_3)\in R$ for all$\; a_1,a_2,a_3 \in A$
- .A relation R is an equivalnce relation if R is reflexive,symmetric and transitive.

Step1:

a R b a is congruant to b $a,b \in T$

$ a R a $ is true since every triangle is congruent t itself

R is reflexive

Step2:

a R b

=> a is congruent to b

=> bis congruent to a

b R a

R is symmetric

Step3:

a R b and b R c

a is congruent to b and b is congruent to c

hence a is congruent to c

a R c

R is transitive

Solution:Hence R is an equivalnce relation

option 'c' is correct

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