https://file.aiquickdraw.com/mathbot/file/1729695557976kzg2swsv.jpg

The question asks what rigid transformation maps triangle \( \triangle A''B''C'' \) to triangle \( \triangle DEF \).

### Key points:
- **Rigid transformations** include **reflection**, **rotation**, and **translation**, as they preserve the shape and size of the figure.
- The given triangles \( \triangle A''B''C'' \) and \( \triangle DEF \) are congruent (as suggested by the context of the problem mentioning AAS, Angle-Angle-Side congruence), so a rigid transformation exists between them.

From the diagram:
- \( \triangle A''B''C'' \) seems to be rotated and translated to match \( \triangle DEF \).
- Given this, the appropriate rigid transformation that maps \( \triangle A''B''C'' \) to \( \triangle DEF \) is most likely **rotation**.

Thus, the correct answer is:

**Rotation**.

Would you like further details on AAS or rigid transformations? Here are some follow-up questions:

1. What is the definition of AAS (Angle-Angle-Side) congruence?
2. How does a rotation transformation differ from a reflection?
3. What are the properties preserved in a rigid transformation?
4. Can a dilation be a rigid transformation? Why or why not?
5. How do you determine the center of rotation in a geometric transformation?

### Tip:
Rigid transformations (reflection, rotation, and translation) always preserve distances and angles, meaning the image is congruent to the preimage.

What rigid transformation maps triangle A''B''C'' to triangle DEF?

Explore how rigid transformations map triangle A''B''C'' to triangle DEF using rotation. This geometry problem demonstrates the principles of AAS congruence and rigid transformations, suitable for students in Grades 8-10.

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