Let T be the set of all triangles in the Euclidean plane and let a re…

The correct answer is Option (3) → equivalence ##

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 reflexive, --- (i)

Let $aRb \Rightarrow a \cong b$

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

So, $R$ is 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, $R$ is equivalence relation.