Given a right triangle $ABC$ and its translated image $A\text{'}B\text{'}C\text{'}$, which of the following statements is true?

• A. The measures of the corresponding angles in $ABC$ and $A\text{'}B\text{'}C\text{'}$ are different.
• B. The orientation of $ABC$ changes after translation.
• C. The corresponding side lengths of $ABC$ and $A\text{'}B\text{'}C\text{'}$ are equal.
• D. The ratios of the side lengths in $ABC$ and $A\text{'}B\text{'}C\text{'}$ are not preserved.

Answer: (C)

Verified step by step guidance

1. Recall that a translation is a type of rigid transformation that slides a figure without rotating or resizing it.
2. Understand that because translation does not change the size or shape of a figure, the measures of corresponding angles remain the same.
3. Recognize that the orientation of the triangle does not change after translation since the figure is only shifted, not flipped or rotated.
4. Know that corresponding side lengths in the original triangle and its translated image are equal because translation preserves distances.
5. Conclude that the ratios of side lengths are preserved as well, since the side lengths themselves remain unchanged.