To show that triangle ABC is congruent to triangle EFD (△ABC ≅ △EFD) by mapping one triangle on top of the other, we generally consider transformations such as dilation, rotation, translation, and reflection.
- Transformations Required:
- Translation: This is often necessary to move the triangles so that corresponding points or sides coincide.
- Rotation: This may be needed to align the triangles properly after translation.
- Reflection: This may be required if the orientation of the triangles is opposite after translation and rotation.
Dilation is typically not needed for triangle congruency, as it changes the size of the figure rather than maintaining congruence.
Possible necessary transformations: Translation, Rotation, and possibly Reflection (check all that apply based on the specifics of △ABC and △EFD).
- Theorem Justification: The transformations used to establish triangle congruence depend on how you relate the two triangles.
- If you used Side-Angle-Side (SAS) or Angle-Side-Angle (ASA) to demonstrate that the corresponding sides and angles are equal after applying the transformations, you would select those theorems respectively.
Without knowing the specific measurements or relationships between the triangles, it is reasonable to say that SAS or ASA could be justified, depending on whether two sides and the included angle, or two angles and the included side were used.
Ultimately, the responses would be:
- Transformations: Translation, Rotation, and possibly Reflection.
- Theorem Justification: SAS or ASA (based on details of the triangles).
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