The text describes a geometric problem where $E, F,$ and $G$ are three non-aligned points. The instructions are about constructing perpendicular lines to certain segments through specific points. Here's a breakdown of the tasks based on the handwriting:

1. Draw Line $EF$: Construct the line segment connecting points $E$ and $F$.

2. Draw a Line Perpendicular to $EF$ Passing Through $G$:

   • Construct a perpendicular line to the segment $EF$ at the location of point $G$.

3. Draw Line $EG$: Connect points $E$ and $G$ with a straight line.

4. Draw a Line Perpendicular to $EG$ Passing Through $F$:

   • Construct a line that is perpendicular to the segment $EG$ at point $F$.

5. Draw Line $FG$: Connect points $F$ and $G$ with a straight line.

6. Draw a Line Perpendicular to $FG$ Passing Through $E$:

   • Construct a perpendicular line to the segment $FG$ at point $E$.

This exercise focuses on mastering the concepts of perpendicularity and line construction in geometry.

Would you like detailed steps for any of these constructions or additional explanations?

Related Questions:

1. What tools are required to construct perpendicular lines in geometry?
2. How can you confirm two lines are perpendicular?
3. What are the properties of perpendicular lines in a plane?
4. Can a triangle be formed by connecting $E, F,$, and $G$, and if so, what type?
5. What is the significance of using perpendicular constructions in geometric problems?

Tip: Always use a compass and ruler to ensure precision in constructing perpendicular lines.