Calculation:

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

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

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

Since, \(\displaystyle\triangle{G}{H}{I}\sim\triangle{D}{E}{F}\) then,

\(\displaystyle\frac{{{G}{H}}}{{{D}{E}}}=\frac{{{H}{I}}}{{{E}{F}}}\)

\(\displaystyle=\frac{{{G}{I}}}{{{D}{F}}}\)

If all sides of the triangle are similar then, its angles are also similar to each other.

Then, the triangles \(\displaystyle\triangle{A}{B}{C}\sim\triangle{G}{H}{I}\) since, the triangle \(\displaystyle\triangle{D}{E}{F}\) is similar in both the triangle by SAS similarity.

Therefore, the triangle ABC and GHI are similar to each other by SAS similarity.

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

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

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

Since, \(\displaystyle\triangle{G}{H}{I}\sim\triangle{D}{E}{F}\) then,

\(\displaystyle\frac{{{G}{H}}}{{{D}{E}}}=\frac{{{H}{I}}}{{{E}{F}}}\)

\(\displaystyle=\frac{{{G}{I}}}{{{D}{F}}}\)

If all sides of the triangle are similar then, its angles are also similar to each other.

Then, the triangles \(\displaystyle\triangle{A}{B}{C}\sim\triangle{G}{H}{I}\) since, the triangle \(\displaystyle\triangle{D}{E}{F}\) is similar in both the triangle by SAS similarity.

Therefore, the triangle ABC and GHI are similar to each other by SAS similarity.