Angle-Angle similarity criterion states that if two angles of one triangle are equal to two angles of another triangle, the triangles are similar.

In \(\displaystyle\triangle{A}{V}{B}{\quad\text{and}\quad}\triangle{N}{V}{K}\),

\(\displaystyle\angle{A}=\angle{N}{\quad\text{and}\quad}\angle{V}\) is common angle

So, \(\displaystyle\triangle{A}{V}{B}\sim\triangle{N}{V}{K}\) by Angle-Angle similarity theorem.

Hence,the theorem that justifies the given statement is Angle-Angle similarity theorem.

In \(\displaystyle\triangle{A}{V}{B}{\quad\text{and}\quad}\triangle{N}{V}{K}\),

\(\displaystyle\angle{A}=\angle{N}{\quad\text{and}\quad}\angle{V}\) is common angle

So, \(\displaystyle\triangle{A}{V}{B}\sim\triangle{N}{V}{K}\) by Angle-Angle similarity theorem.

Hence,the theorem that justifies the given statement is Angle-Angle similarity theorem.