The image provides two geometric relationships:

1. Problem 6: $\overline{DG} \parallel \overline{MS}$

   • This indicates that the two line segments $\overline{DG}$ and $\overline{MS}$ are parallel to each other. You should draw two distinct line segments and mark them with parallel line symbols (like small triangles or arrows).

2. Problem 7: $\overline{PE} \perp \overline{AR}$

   • This specifies that the two line segments $\overline{PE}$ and $\overline{AR}$ are perpendicular. You would draw these two line segments forming a right angle and use a square mark at the intersection to denote the 90-degree angle.

To draw:

1. For problem 6, draw two non-intersecting line segments, marking them as parallel using the appropriate symbol.
2. For problem 7, draw two lines that intersect at a right angle, marking the right angle.

Would you like me to further explain how to draw these, or provide any additional details?

Here are five related questions:

1. How do you prove two lines are parallel in a coordinate plane?
2. What properties define perpendicular lines in geometry?
3. Can parallel lines intersect under any circumstances in non-Euclidean geometry?
4. How do congruent segments differ from parallel lines in terms of their properties?
5. What geometric postulate guarantees the uniqueness of a perpendicular line through a point?

Tip: When drawing geometric figures, use symbols like small triangles for parallelism and a small square to represent right angles to maintain clarity.