Calculation:

The given similar triangle is \(\displaystyle\triangle{A}{D}{C}\sim\triangle{B}{E}{C}\). And this is only possible \(\displaystyle\overline{{{A}{D}}}{\quad\text{and}\quad}\overline{{{E}{B}}}\) are parallel.

Therefore, \(\displaystyle\angle{C}{A}{D}{\quad\text{and}\quad}\angle{C}{D}{A}\) is equal to the \(\displaystyle\angle{C}{B}{E}{\quad\text{and}\quad}\angle{C}{E}{B}\), so that the triangle is similar by AA-similarity

Hence, the correct option is (C).

The given similar triangle is \(\displaystyle\triangle{A}{D}{C}\sim\triangle{B}{E}{C}\). And this is only possible \(\displaystyle\overline{{{A}{D}}}{\quad\text{and}\quad}\overline{{{E}{B}}}\) are parallel.

Therefore, \(\displaystyle\angle{C}{A}{D}{\quad\text{and}\quad}\angle{C}{D}{A}\) is equal to the \(\displaystyle\angle{C}{B}{E}{\quad\text{and}\quad}\angle{C}{E}{B}\), so that the triangle is similar by AA-similarity

Hence, the correct option is (C).