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In this problem, you're asked to identify which triangles are translations of triangle \( X \). A translation involves sliding a shape to a different position without rotating, resizing, or flipping it. This means the translated triangle must have the same shape, size, and orientation as triangle \( X \).

To solve this:

- **Triangle X** is a right-angled triangle, with a small acute angle on the left and a longer side slanting down to the right.
- The translated triangles will be identical in shape and size, and their orientation will be the same as triangle \( X \), just moved to a different location on the grid.

### Analysis of the triangles:
- **Triangle A**: This triangle appears to be smaller and does not match the size of triangle \( X \).
- **Triangle B**: This triangle appears to be rotated compared to triangle \( X \).
- **Triangle C**: This triangle appears to be smaller and rotated compared to triangle \( X \).
- **Triangle D**: This triangle is the same size, shape, and orientation as triangle \( X \), so it is a translation.
- **Triangle E**: This triangle appears to be smaller and does not match the size of triangle \( X \).
- **Triangle F**: This triangle is the same size, shape, and orientation as triangle \( X \), so it is a translation.
- **Triangle G**: This triangle appears to be rotated compared to triangle \( X \).

### Conclusion:
The triangles that are translations of triangle \( X \) are **Triangles D** and **F**.

Would you like further details or have any questions?

Here are 5 follow-up questions you might consider:
1. How is a translation different from a reflection or rotation?
2. What would happen to the coordinates of a shape if it is translated on a coordinate plane?
3. How can you mathematically describe a translation in terms of vectors?
4. What are some real-life applications where translations are used?
5. How can you confirm a shape has been translated and not reflected or rotated?

**Tip**: When identifying translations, always check that the shape and size are exactly the same and ensure there is no change in orientation.

Select all of the triangles below which are translations of triangle X.

Learn how to identify which triangles are translations of a given triangle on a grid. This exercise focuses on translation geometry concepts and congruence. Suitable for students in Grades 6-8.

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