The image shows a geometric exercise titled "Figure papillon" (Butterfly figure). Here's a breakdown of the problem and how to approach solving it.

Part a:

You are asked to observe the figure and fill in the blanks with either ∈ (belongs to) or ∉ (does not belong to) in the given sentences.

Based on the diagram:

• $G \, \underline{\phantom{e}} \, [AU]$
• $A \, \underline{\phantom{e}} \, [GU]$
• $S \, \underline{\phantom{e}} \, [RG]$
• $G \, \underline{\phantom{e}} \, [AU]$
• $U \, \underline{\phantom{e}} \, [AG]$
• $S \, \underline{\phantom{e}} \, [RG]$

In this exercise, you need to check whether each point lies on the respective segment.

Part b:

This part asks which points are aligned (collinear) and requires two sentences about the alignment of the points in the figure.

Part c:

The task here is to define point G, which is likely an important point related to the geometric configuration.

Detailed Steps:

1. For Part a:

   • Look at the diagram and determine whether each point lies on the segment by checking its position relative to the line segments.

2. For Part b:

   • Identify the points that lie on the same straight line by visual inspection. For example, if points A, G, and U are on the same straight segment, they are collinear.

3. For Part c:

   • Point G might be defined as an intersection point of certain lines or segments in the figure. Based on the structure, G could be the intersection of diagonals or sides of a specific shape.

Would you like help with detailed solutions for each part or clarifications?

Here are some related questions to expand your understanding:

1. What does it mean for points to be collinear in geometry?
2. How do you determine if a point belongs to a segment?
3. How is the midpoint of a segment defined, and is G possibly a midpoint here?
4. Can the butterfly figure be divided into any triangles or other geometric shapes?
5. What role do diagonals play in geometric configurations like this one?

Tip: When dealing with geometric figures, always look for symmetries and intersections of key segments to better understand the relationships between points.