The image shows a triangle with angles expressed algebraically and a line segment labeled as $\overline{GE}$. To determine the correct description for $\overline{GE}$, let's analyze the figure:

• The triangle is isosceles, as evidenced by the two equal angles at $\angle DGE$ and $\angle FGE$ (marked by the same number of tick marks).
• These equal angles suggest that $\overline{GE}$ is likely an angle bisector, since it divides the vertex angle at $E$ into two equal parts.
• The other options, like perpendicular bisector, median, altitude, and hypotenuse, do not seem to match the properties of $\overline{GE}$.

Based on this, the most likely description of $\overline{GE}$ is angle bisector.

Let me know if you'd like further explanation or if you have more questions!

Here are 5 related questions for further exploration:

1. What is the definition of an angle bisector in a triangle?
2. How can you identify if a line is a median in a triangle?
3. What is the difference between a perpendicular bisector and an angle bisector?
4. How do the properties of an isosceles triangle affect its angle bisectors?
5. How do you calculate the length of a median in a triangle?

Tip: Remember that in an isosceles triangle, the angle bisector of the vertex angle also acts as the perpendicular bisector of the base!