Step 1:

Reflexitivity :

We know every triangle is congruent to itself.

$\therefore (T,T)\in R$ all $T\in A$

$\Rightarrow R$ is reflexive.

Step 2:

Symmetry :

Let $(T_1,T_2)\in R$ then

$(T_1,R_2)\in R$

$T_1$ is congruent to $T_2$

$\Rightarrow T_2$ is congruent to $T_1$

$\Rightarrow (T_2,T_1)\in R$

So $R$ is symmetric.

Step 3:

Transitivity :

Let $T_1,T_2,T_3\in A$ .such that $(T_1,T_2)\in R$ and $(T_2,T_3)\in R$

Then $(T_1,T_2)\in R$ and $(T_2,T_3)\in R$

$\Rightarrow T_1$ is congruent to $T_2$ and $T_2$ is congruent to $T_3$

$\Rightarrow T_1$ is congruent to $T_3$

$\therefore (T_1,T_3)\in R$

So $R$ is transitive.

Hence $R$ is an equivalence relation.