Final answer:
Only translation (option C) preserves the angles and side lengths of Triangle ABC by sliding the figure without altering its shape or size.
Step-by-step explanation:
The transformation applied to Triangle ABC that would preserve its angles and side lengths is C) Translation 3 units to the left. A translation involves sliding the entire figure in a specific direction for a certain distance without changing its shape or size. Unlike translations, dilations and stretches change the size of the original figure, hence altering the side lengths. A dilation by a scale factor of 2 (option A) would increase the size of the triangle, so the side lengths would be doubled. Both a horizontal stretch (option B) and a vertical stretch (option D) would also alter the original side lengths by stretching them only in one direction.