To show that triangle \( \triangle ABC \) is congruent to triangle \( \triangle EFD \) by mapping \( ABC \) on top of \( EFD \), the following transformations could be needed:
- Rotation: This could be necessary if the orientation of the triangles is different.
- Translation: This is often needed to position one triangle over the other.
- Reflection: This could be required if the triangles are mirror images of each other.
- Dilation: This would not apply, as dilation changes the size of the triangle and is not a congruence transformation.
Based on that analysis, the necessary transformations could include Rotation, Translation, and Reflection.
For Question 2, the theorem that justifies the congruence of the triangles after applying transformations would depend on how the triangles can be mapped. In this case, if we can prove that the sides and angles correspond using transformations, the most applicable theorem would be:
- SAS (Side-Angle-Side), if two sides and the angle between them are shown to be equal.
However, without specific lengths or angle measures provided, it’s challenging to select the definitive theorem. But if congruence is established through sides and angles:
Final Answers:
- Possible transformations: Rotation, Translation, Reflection
- The theorem that justifies the congruence: SAS (assuming side-angle configurations are evident).