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To analyze the given problem, we need to understand the relationship between triangle \( \triangle DEF \) and its transformed counterpart \( \triangle D'E'F' \).

### Step 1: Identifying the Transformation
Looking at the coordinates of points \( D \), \( E \), and \( F \), as well as \( D' \), \( E' \), and \( F' \), it appears that the transformation relates to a reflection across one of the axes.

### Step 2: Checking the Reflection Across the x-axis and y-axis
- **Reflection across the x-axis**: In this case, the y-coordinates would change signs (e.g., \( (x, y) \) would become \( (x, -y) \)).
- **Reflection across the y-axis**: Here, the x-coordinates would change signs (e.g., \( (x, y) \) would become \( (-x, y) \)).

The provided image and selection indicate that the answer chosen was "Using a reflection across the y-axis, which is a rigid motion." This is consistent with mapping the original triangle \( \triangle DEF \) to the reflected triangle \( \triangle D'E'F' \) since their coordinates show a change in the signs of the x-coordinates.

Thus, the answer "Using a reflection across the y-axis, which is a rigid motion" is correct.

Which statement correctly describes the relationship between triangles DEF and D'E'F'?

Understand how to determine the relationship between triangles DEF and D'E'F' through a reflection across the y-axis. This problem focuses on congruence, rigid motions, and transformations, making it ideal for geometry students in Grades 8-10.

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