Final answer:
To prove congruence between two triangles using rigid motions, one can perform a translation, a rotation, a reflection, or a combination of these motions ensuring that the original triangle perfectly overlays the second triangle.
Step-by-step explanation:
To describe a sequence of rigid motions that would prove a congruence between triangles ABC and A'B'C', one can perform the following actions:
- a) Translation only: Slide triangle ABC along a straight path without rotating it until it coincides with triangle A'B'C'.
- b) Rotation only: Rotate triangle ABC around a fixed point until it aligns with triangle A'B'C'. The center of rotation and the angle of rotation must be chosen appropriately.
- c) Reflection only: Flip triangle ABC over a line (the line of reflection) so that it mirrors onto triangle A'B'C'.
- d) Combination of translation, rotation, and reflection: Perform a translation to bring the triangles closer together, then a rotation to align them, followed by a reflection if necessary to ensure that they overlap perfectly.
These actions rely on the concepts of kinematics involving translational and rotational motion.