Final answer:
The rigid transformations that can map triangle ABC onto triangle DEC are reflection, then rotation; reflection, then translation; and rotation, then translation.
Step-by-step explanation:
The transformations that can map triangle ABC onto triangle DEC are:
- Reflection, then rotation: Reflection over a line followed by a rotation about a point can transform one triangle into another. For example, you could reflect triangle ABC over a line to create triangle A'B'C', and then rotate triangle A'B'C' around a point to obtain triangle DEC.
- Reflection, then translation: Reflection over a line followed by a translation can also map one triangle onto another. In this case, you could reflect triangle ABC over a line to obtain triangle A'B'C', and then translate triangle A'B'C' to get triangle DEC.
- Rotation, then translation: Alternatively, you could rotate triangle ABC about a point to create triangle A'B'C', and then translate triangle A'B'C' to obtain triangle DEC.
It is not possible to map triangle ABC onto triangle DEC using rotation followed by dilation.