Question

To show how AAS follows from the definition of congruence, answer the following question. What rigid transformation maps △A" B" C" → △DEF ?
dilation
rotation
reflection
translation

Answer 1

To determine which rigid transformation maps triangle \( \triangle A'B'C' \) to triangle \( \triangle DEF \), we need to understand what "rigid transformation" means. Rigid transformations include rotations, reflections, and translations, which preserve the shape and size of the figures.

If the triangles \( \triangle A'B'C' \) and \( \triangle DEF \) are congruent, this means there exists a sequence of rigid transformations that maps one triangle onto the other.

1. **Dilation** is not a rigid transformation because it changes the size of the figure.
2. **Rotation** can map one triangle to another if the triangles are oriented differently but have the same size and shape.
3. **Reflection** can also map one triangle to another if they are mirror images of each other.
4. **Translation** can move one triangle to another if they are in the same orientation and position.

To specifically determine which transformation is needed, we would look at the positions, orientation, and sizes of the triangles:

- If \( \triangle DEF \) is directly superimposed on \( \triangle A'B'C' \) without needing to turn, flip, or resize, then **translation** is the transformation.
- If the triangles are oriented differently but same-size, then **rotation** is the correct choice.
- If one triangle is a mirror image of the other, then **reflection** is necessary.

In conclusion, without additional context about the triangles' positions and orientations, a general answer cannot be definitively stated. The answer would depend on the specific geometric relationship between \( \triangle A'B'C' \) and \( \triangle DEF \).