Question

1. order the sides of δdef from shortest to longest.

a. de
b. df
c. ef

Explanation:

Step1: Find the third angle

In a triangle, the sum of interior angles is \(180^\circ\). Given \(\angle E = 60^\circ\) and \(\angle F = 70^\circ\), then \(\angle D=180^\circ - 60^\circ - 70^\circ = 50^\circ\).

Step2: Relate angles to sides

In a triangle, the larger the angle, the longer the side opposite to it. The angles in \(\triangle DEF\) are \(\angle D = 50^\circ\), \(\angle E = 60^\circ\), \(\angle F = 70^\circ\). So, \(\angle D<\angle E<\angle F\). The sides opposite these angles are \(EF\) (opposite \(\angle D\)), \(DF\) (opposite \(\angle E\)), and \(DE\) (opposite \(\angle F\)) respectively. Thus, the order from shortest to longest is \(EF\), \(DF\), \(DE\).

Answer:

EF, DF, DE