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 congruent to b ∀ a, b ∈ T. Then R is

The correct option is equivalence.

To determine if a relation $R$ defined on a set $T$ is an equivalence relation, we must verify if it satisfies three fundamental properties: reflexivity, symmetry, and transitivity. Let $T$ be the set of all triangles in the Euclidean plane, and let $R$ be the relation defined by:
$aRb$ if and only if triangle $a$ is congruent to triangle $b$, denoted as $a\cong b$, for all $a,b\in T$.

1. Reflexivity:
A relation $R$ is reflexive if every element is related to itself. That is, for any triangle $a\in T$, we must have $aRa$.
Since any triangle is geometrically identical to itself in shape and size, every triangle is congruent to itself ($a\cong a$).
Therefore, $aRa$ holds true for all $a\in T$, which means the relation $R$ is reflexive.

2. Symmetry:
A relation $R$ is symmetric if $aRb$ implies $bRa$ for all $a,b\in T$.
If triangle $a$ is congruent to triangle $b$ ($a\cong b$), it means that by translating, rotating, and/or reflecting triangle $a$, it can be perfectly superimposed on triangle $b$. Consequently, triangle $b$ can also be perfectly superimposed on triangle $a$, which means triangle $b$ is congruent to triangle $a$ ($b\cong a$).
Therefore, $aRb\Rightarrow bRa$, which means the relation $R$ is symmetric.

3. Transitivity:
A relation $R$ is transitive if $aRb$ and $bRc$ imply $aRc$ for all $a,b,c\in T$.
Suppose triangle $a$ is congruent to triangle $b$ ($a\cong b$) and triangle $b$ is congruent to triangle $c$ ($b\cong c$).
Since $a$ has the same side lengths and angles as $b$, and $b$ has the same side lengths and angles as $c$, it directly follows that $a$ has the same side lengths and angles as $c$. Thus, triangle $a$ is congruent to triangle $c$ ($a\cong c$).
Therefore, $aRb$ and $bRc\Rightarrow aRc$, which means the relation $R$ is transitive.

Since the relation $R$ is reflexive, symmetric, and transitive, it is by definition an equivalence relation.