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.