Final answer:
Option 1, involving translation and rotation, and Option 3, involving reflection and translation, are the valid ways to move triangle AABC onto triangle AA'B'C', depending on the triangles' orientations.
Step-by-step explanation:
We have different ways to map one triangle onto another depending on the properties of the given triangles and the nature of the transformation itself. A translation involves sliding a shape in a straight line from one position to another without rotating or flipping it, while a rotation involves turning the shape around a fixed point through a specified angle and direction. In contrast, a dilation involves expanding or contracting the shape proportionally from a center point, and a reflection creates a mirror image of the shape over a line, known as the axis of reflection.
Option 1: Translation and Rotation
By translating triangle AABC so that one of its vertices coincides with one of the corresponding vertices of triangle AA'B'C', and then rotating about this matching point until all vertices align, the two triangles will coincide.
Option 3: Reflection and Translation
Reflecting triangle AABC over a line so that it aligns with triangle AA'B'C' and then translating the reflected triangle to match up with triangle AA'B'C' can also map the two triangles onto one another.
Considering the provided geometric scenarios and transformation methods, Option 1 and Option 3 both describe valid ways to move triangle AABC onto triangle AA'B'C', depending on the specific arrangement and orientation of the triangles.