Let $T$ be the set of all triangles in the Euclidean plane and let a relation $R$ on $T$
be defined as $aRb$, if $a$ is congruent to $b,$ $\forall a,b \in T$. Then, $R$ is

Consider that $aRb$, if $a$ is congruent to $b,\forall a,b \in T$.

Then, $aRa \Rightarrow a \cong a$,

which is true for all $a \in T$

So, $R$ is For reflexive,
……(i)
Let $aRb \Rightarrow a \cong b$

$\Rightarrow$ $b \cong a \Rightarrow b \cong a$
$\Rightarrow$ $$\;bRa$$

So, $R$ is For symmetric. ……(ii)
Let $aRb$ and $bRc$

$\Rightarrow$ $a \cong b$ and $b \cong c$

$\Rightarrow$ $a \cong c \Rightarrow aRc$
So, $R$ is transitive.
……(iii)
Hence we can say that, $R$ is equivalence relation.