Question

To write: the name of the postulate, that justifies the given statement.
Given information:In \(\displaystyle\triangle{A}{V}{B}{\quad\text{and}\quad}\triangle{N}{V}{K},\angle{A}=\angle{N}={60}^{{\circ}}\).
The given figure is as follows:

Answer 1

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.