Which composition of transformations will create a pair of similar, but not congruent, triangles?

• A. A reflection followed by a translation
• B. A rotation followed by a reflection
• C. A translation followed by a rotation
• D. A dilation with a scale factor $>1$ centered at a point, followed by a rotation

Answer: (D)

Verified step by step guidance

1. Understand that similar triangles have the same shape but not necessarily the same size, meaning their corresponding angles are equal and their corresponding sides are proportional.
2. Recall that transformations like reflections, rotations, and translations are rigid motions, which preserve distances and angles, so they produce congruent figures, not just similar ones.
3. Recognize that a dilation changes the size of a figure by a scale factor, which can create similar figures that are not congruent if the scale factor is not 1.
4. Identify that performing a dilation with a scale factor greater than 1 centered at a point will enlarge the triangle, creating a similar triangle that is not congruent to the original.
5. Note that following the dilation with a rotation will preserve similarity because rotations are rigid motions that do not alter size or shape, so the final figure remains similar but not congruent to the original.