In \(\displaystyle\triangle{A}{B}{C}\ {\quad\text{and}\quad}\ \triangle{D}{E}{F}\)

Taking the ratio of sides

\(\displaystyle\Rightarrow{\frac{{{A}{B}}}{{{D}{E}}}}={\frac{{{B}{C}}}{{{E}{F}}}}={\frac{{{C}{A}}}{{{F}{D}}}}\)

\(\displaystyle\Rightarrow{\frac{{{4}}}{{{2}}}}={\frac{{{6}}}{{{3}}}}={\frac{{{2}}}{{{1}}}}={2}\)

So,

The ratio of corresponding sides are equal,

Then, from SSS(side-side-side) rule of similarity

\(\displaystyle\triangle{A}{B}{C}\sim\triangle{D}{E}{F}\)

Taking the ratio of sides

\(\displaystyle\Rightarrow{\frac{{{A}{B}}}{{{D}{E}}}}={\frac{{{B}{C}}}{{{E}{F}}}}={\frac{{{C}{A}}}{{{F}{D}}}}\)

\(\displaystyle\Rightarrow{\frac{{{4}}}{{{2}}}}={\frac{{{6}}}{{{3}}}}={\frac{{{2}}}{{{1}}}}={2}\)

So,

The ratio of corresponding sides are equal,

Then, from SSS(side-side-side) rule of similarity

\(\displaystyle\triangle{A}{B}{C}\sim\triangle{D}{E}{F}\)