https://file.aiquickdraw.com/mathbot/file/1728318961329p6c73by3.jpg

This exercise is based on geometric symmetries. Let’s analyze and complete the sentences from the image using the given diagram.

### Observations:
- The vertical line \( \Delta \) serves as an axis of symmetry, splitting the plane horizontally.
- Line \( MN \) also divides the plane vertically.
- Various points and segments exhibit reflective symmetry across these lines.

### Let's complete the sentences:

1. **"B est le symétrique de... par rapport à \( \Delta \)."**
   - **Answer**: \( A \), because point \( B \) is the reflection of \( A \) across line \( \Delta \).

2. **"..... est le symétrique de I par rapport à (MN)."**
   - **Answer**: \( J \), as point \( J \) is the reflection of point \( I \) across line \( MN \).

3. **"[AE] est le symétrique de.... par rapport à \( \Delta \)."**
   - **Answer**: \( [BF] \), because segment \( [AE] \) is symmetric to segment \( [BF] \) across \( \Delta \).

4. **"La droite (AM) est ... de (BN) par rapport à (..)."**
   - **Answer**: The missing part is "symétrique" and \( \Delta \). So, the answer is "La droite \( (AM) \) est le symétrique de \( (BN) \) par rapport à \( \Delta \)."

5. **"... est le symétrique de l'angle \( \widehat{MIN} \) par rapport à (MN)."**
   - **Answer**: \( \widehat{MJN} \), as it is the reflection of \( \widehat{MIN} \) across line \( MN \).

6. **"AME est le symétrique du triangle... par rapport à \( \Delta \)."**
   - **Answer**: \( BNF \), as triangle \( AME \) is symmetric to triangle \( BNF \) across line \( \Delta \).

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### Would you like any clarifications or additional details about the concepts? Here are five related questions to consider:

1. How can we identify symmetry in geometric figures?
2. What is the importance of an axis of symmetry in geometry?
3. How do transformations like reflections affect the properties of shapes?
4. Can two different axes of symmetry exist for a single geometric shape?
5. How are angles transformed during reflections?

**Tip**: Always verify the position of points with respect to the symmetry axis to avoid errors when determining the reflection.

The geometric exercise involves completing sentences based on the given diagram involving symmetrical reflections across lines.

In this exercise, explore symmetry and reflection across lines, focusing on identifying symmetric points and segments from the given geometric figure. Ideal for students in Grades 6-8, it covers key concepts like symmetry with respect to axes.

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