Question

value: 5
the sides in order from shortest to longest for the triangle below are $overline{uw}$, $overline{uv}$, $overline{vw}$
true
false

Explanation:

Step1: Recall angle - side relationship

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

Step2: Identify angle - side pairs

The angle opposite $\overline{UW}$ is $\angle V = 30^{\circ}$, the angle opposite $\overline{UV}$ is $\angle W=40^{\circ}$, and the angle opposite $\overline{VW}$ is $\angle U = 110^{\circ}$.

Step3: Order sides by length

Since $30^{\circ}<40^{\circ}<110^{\circ}$, the sides in order from shortest to longest are $\overline{UW},\overline{UV},\overline{VW}$.

Answer:

True