The correct answer is C: "It must be an equilateral triangle with the same side lengths as the original triangle."

Explanation:

Transformations like rotations, reflections, and translations are rigid transformations. This means they do not change the shape or size of the figure being transformed. An equilateral triangle, when subjected to these transformations, will remain equilateral with the same side lengths and angles as the original.

Here's why the other options are incorrect:

• A: A scalene triangle with different side lengths would imply a change in both shape and size, which rigid transformations do not allow.
• B: While the triangle would remain equilateral, the side lengths cannot change in a rigid transformation.
• D: An obtuse triangle would not maintain the original shape of an equilateral triangle, which contradicts the nature of rigid transformations.

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Related Questions:

1. What are rigid transformations and how do they affect geometric shapes?
2. Can a triangle change from equilateral to another type under any transformations?
3. How do rotations and reflections specifically affect an equilateral triangle?
4. Why do translations not change the dimensions of geometric figures?
5. What transformations could change an equilateral triangle's dimensions if they existed?

Tip: Rigid transformations always preserve the size, shape, and angles of a figure.