https://file.aiquickdraw.com/mathbot/file/1727456868447nztpjkvo.jpg

The question asks what rigid transformation maps the triangle \( \triangle A''B''C'' \) to \( \triangle DEF \). Rigid transformations are operations that preserve the size and shape of geometric figures, and they include translation, rotation, and reflection.

In the image provided:
- \( \triangle A''B''C'' \) and \( \triangle DEF \) appear congruent.
- The two triangles are oriented in such a way that \( \triangle A''B''C'' \) seems to be a reflection of \( \triangle DEF \) over a line (likely the one containing point \( F \), indicating the axis of reflection).

### Conclusion:
The correct rigid transformation is **reflection**.

Would you like further details or have any questions about this? Here are some related questions to consider:

1. What is a rigid transformation, and how does it differ from non-rigid transformations like dilation?
2. Can a combination of rigid transformations (e.g., reflection and translation) map one triangle to another?
3. How does the Angle-Angle-Side (AAS) postulate ensure congruence between two triangles?
4. What other types of triangle congruence criteria (like SSS or SAS) exist?
5. How can you identify the axis of reflection in a geometric figure?

**Tip**: In geometry, reflections always occur over a line, which acts as the "mirror" between the original and reflected figures.

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

Learn how to identify the rigid transformation that maps triangle ∆A''B''C'' to triangle ∆DEF using the reflection property. This geometry problem covers triangle congruence and the AAS theorem, suitable for students in Grades 8-10.

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