Final answer:
Rotation, reflection, and translation all result in triangles that are both similar and congruent to the original, because they preserve the shape and size of the triangle. Dilation changes the size of the triangle, maintaining the shape but not the size, which results in a figure that is similar but not congruent.
Step-by-step explanation:
The question asks which transformation will create both a similar and a congruent triangle. The transformations that can be applied to a triangle to produce another triangle are rotation, reflection, dilation, and translation. To clarify, a similar triangle maintains the same shape but can have a different size, whereas a congruent triangle is identical in shape and size to the original.
The transformation that creates a congruent triangle is rotation, where the triangle is turned around a fixed point. The same goes for reflection, where the triangle is flipped over a line, and translation, where the triangle is slid from one position to another without changing its orientation or size. These three transformations preserve the angles and side lengths of the original triangle, making it congruent to the result. On the other hand, a dilation scales the triangle up or down, altering the size but maintaining the proportion of side lengths, which produces a similar triangle but not a congruent one. Therefore, rotation, reflection, and translation would produce both similar (if you consider congruent figures as similar) and congruent triangles, while dilation creates only similar triangles.