Question

determine if triangle abc and triangle def are or are not similar, and, if they are, state how you know. (note that figures are not necessarily drawn to scale.) answer the triangles similar.

Explanation:

Step1: Check angle - equality

We see that $\angle C=\angle F = 104^{\circ}$.

Step2: Check side - ratio

Calculate the ratio of corresponding sides. $\frac{EF}{BC}=\frac{34}{17} = 2$ and $\frac{DF}{AC}=\frac{46}{23}=2$.
Since the ratio of the corresponding sides adjacent to the equal angles are equal, by the Side - Angle - Side (SAS) similarity criterion, the triangles are similar.

Answer:

are, by the SAS similarity criterion