Question

Which of the following describes GE check all that applyDF=18

Answer 1

Since DF=18; then,

$\begin{gathered} DF=18 \\ \text{and} \\ DF=FG+GD \\ \Rightarrow FG+GD=18 \\ \Rightarrow3a+a+6=18 \\ \Rightarrow4a=12 \\ \Rightarrow a=3 \\ \end{gathered}$

Therefore,

$\begin{gathered} \Rightarrow FG=9,GD=9 \\ \Rightarrow\Delta\text{EFG}\cong\Delta EDG \end{gathered}$

$\begin{gathered} \Rightarrow\angle FEG\cong\angle\text{DEG} \\ \Rightarrow EG\text{ is angle bisector of }\angle E \end{gathered}$

Furthermore, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. As we proved above, G is the midpoint of segment FD; thus, GE is a median of triangle DEF.

However, we do not have any information regarding the angles besides

Hence, the answers are Angle bisector and Median.