Question

determine whether the pair of triangles is similar. explain your reasoning.
select choice
no
select choice
△acb ~ △dcf by aa similarity
the triangles would be similar by aa similarity if segment ab ∥ segment df
△acb ~ △fcd by aa similarity
need help
get a hint

Explanation:

Step1: Identify vertical angles

$\angle ACB$ and $\angle FCD$ are vertical - angles. So, $\angle ACB=\angle FCD$ (vertical angles are equal).

Step2: Consider AA - similarity condition

For the AA (Angle - Angle) similarity criterion, we need another pair of equal angles. If $AB\parallel DF$, then $\angle A=\angle D$ (alternate interior angles). With $\angle ACB=\angle FCD$ and $\angle A = \angle D$, by the AA similarity criterion, $\triangle ACB\sim\triangle DCF$.

Answer:

The triangles would be similar by AA Similarity if segment AB $\parallel$ segment DF