https://file.aiquickdraw.com/mathbot/file/1729342881897ygkxrf0t.jpg

The task is to determine which shapes (labeled A to H) can be formed by a single reflection of shape \( X \) (the original shape on the left).

### Analysis:
A reflection can be done across either a vertical or horizontal axis. Let’s break this down:

1. **Original Shape \( X \)**: 
   - It is an "L" shape made up of 5 squares.
   - The right side has two squares extending horizontally.
   - There are two main axes we can reflect over: 
     - **Vertical reflection** (over a line going through the middle vertically).
     - **Horizontal reflection** (over a line going through the middle horizontally).

2. **Identifying Reflections**:
   - **Vertical reflection** will flip the two squares that extend horizontally to the left.
   - **Horizontal reflection** will flip the two squares that extend horizontally downward.

### Step-by-Step Evaluation of Shapes A to H:
- **Shape A**: This is the original \( X \) reflected horizontally. **Valid reflection.**
- **Shape B**: This shape is similar to \( X \) but rotated; it's not a reflection. **Not valid.**
- **Shape C**: This shape appears as the result of a vertical reflection of \( X \). **Valid reflection.**
- **Shape D**: This is neither a horizontal nor vertical reflection of \( X \). **Not valid.**
- **Shape E**: This appears to be a rotated version of \( X \), but it's not a simple reflection. **Not valid.**
- **Shape F**: This is a vertically reflected version of \( X \). **Valid reflection.**
- **Shape G**: This is not a valid reflection of \( X \). **Not valid.**
- **Shape H**: This is the original \( X \) reflected horizontally. **Valid reflection.**

### Conclusion:
The shapes that can be formed by a single reflection of shape \( X \) are **A, C, F, H**.

Let me know if you'd like further details or have any questions!

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**Related Questions:**
1. How would rotating the shape \( X \) affect which shapes are formed?
2. Can you explain the difference between rotation and reflection in geometry?
3. What other transformations (besides reflection) could result in shapes like \( X \)?
4. How do symmetry properties relate to reflections of geometric shapes?
5. Can a combination of reflection and rotation form the other shapes?

**Tip**: When performing geometric transformations, visualize the axes and how the shape behaves across different reflections or rotations.

Select all of the shapes below that can be formed by a single reflection of shape X.

Explore which shapes can be formed by a single reflection of shape X. This geometry problem focuses on reflections and symmetry, making it suitable for middle school students (Grades 6-8). Learn the steps to analyze and identify the valid reflected shapes.

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