Chapter 4.7, Problem 8CE

a)

To determine

Whether the median drawn from $F$ to $\overline{DE}$ be the same segment as $\overline{FX}$ .

Explanation of Solution

Given information:

$\Delta DEF$ is isosceles with $DE=EF$ ;

$\overline{FX}$ bisects $\angle DEF$ .

Given figure,

Calculation:

Consider the following data:

Triangle $\Delta DEF$ is isosceles with $DE=EF$ ;

$\overline{FX}$ bisects $\angle DEF$ .

Yes, the median drawn from $F$ to $\overline{DE}$ be the same segment as $\overline{FX}$ because point $F$ lies on the bisector of $\angle DEF$ .

Therefore, point $F$ is equidistant from the sides of $\angle DEF$ or $\overline{FX}$ is the median of $\Delta DEF$

b)

To determine

Whether the altitude drawn from $F$ to $\overline{DE}$ be the same segment as $\overline{FX}$ .

Explanation of Solution

Given information:

$\Delta DEF$ is isosceles with $DE=EF$ ;

$\overline{FX}$ bisects $\angle DEF$ .

Given figure,

Calculation:

Consider the following data:

Triangle $\Delta DEF$ is isosceles with $DE=EF$ ;

$\overline{FX}$ bisects $\angle DEF$ .

Yes, the altitude drawn from $F$ to $\overline{DE}$ be the same segment as $\overline{FX}$ because point $F$ is equidistant from the sides of $\angle DEF$ .

Therefore, point $F$ lies on the bisector of $\angle DEF$ or $\overline{FX}$ is the altitude of $\Delta DEF$ .