Chapter 6, Problem 9CT

To determine

To find: the shortest segment of the given figure.

Answer to Problem 9CT

The shortest segment is $\overline{GE}$ .

Explanation of Solution

Given information:

The given figure is as follows:

  

Calculation:

Sum of the interior angles of triangle $={180}^0.$

  $\begin{array}{l}m\angle DEG={180}^0-{60}^0-{61}^0={59}^0\\ m\angle GEF={180}^0-{62}^0-{55}^0={63}^0\end{array}$

In the given triangle, $\angle F$ is smallest angle.

The side opposite to the smallest angle is the smallest segment.

Thus, the side opposite to the $\angle F$ is $\overline{GE}$ .

Hence, the shortest segment is $\overline{GE}$ .