Show that the relation R defined in the set A of all triangles as R =…

R= {$(T_1, T_2)$: $T_1$ is similar to $T_2$}

R is reflexive since every triangle is similar to itself.

Further, if $(T_1, T_2) ∈ R$, then T, is similar to $T_2$.

⇒ $T_2$ is similar to $T_2$

$⇒ (T_2, T_1) ∈ R$.

Therefore, R is symmetric.

Now, let $(T_1, T_2), (T_2, T_3) ∈ R$.

⇒ $T_1$ is similar to $T_2$ and $T_2$ is similar to $T_3 $

⇒ $T_1$ is similar to $T_3$

$⇒ (T_1, T_3) ∈ R$

Therefore, R is transitive.

Thus, R is an equivalence relation.