Question

order the side lengths de, ef, and fd from least to greatest. (note that the figure is not drawn to scale.)

Explanation:

Step1: Find angle F

Use the angle - sum property of a triangle ($\angle E+\angle D+\angle F = 180^{\circ}$). Given $\angle E = 66^{\circ}$ and $\angle D=45^{\circ}$, then $\angle F=180^{\circ}-66^{\circ}-45^{\circ}=69^{\circ}$.

Step2: Recall the side - angle relationship

In a triangle, the side opposite the smallest angle is the shortest and the side opposite the largest angle is the longest.

Step3: Order the sides

Since $\angle D = 45^{\circ}<\angle E=66^{\circ}<\angle F = 69^{\circ}$, the side opposite $\angle D$ is $EF$, the side opposite $\angle E$ is $FD$, and the side opposite $\angle F$ is $DE$. So, $EF

Answer:

$EF