To show that triangles \( \triangle ABC \) is congruent to \( \triangle EFD \) by mapping \( ABC \) on top of \( EFD \), the following transformations can apply:
Question 1:
Responses:
- Dilation: Not necessary for congruence, as it changes the size of the triangle.
- Rotation: This is a valid transformation. If the triangles are oriented differently, a rotation can align them.
- Translation: This is also a valid transformation. Moving the triangle without changing its shape can help position it on top of the other triangle.
- Reflection: This can also be a valid transformation. If the triangles are mirror images, a reflection can help realign them.
Correct Responses:
- Rotation
- Translation
- Reflection
(Note: Dilation is not needed for congruence as it changes the size of the triangle. The three congruent transformations involved are rotation, translation, and reflection.)
Question 2:
The transformations that show \( \triangle ABC \cong \triangle EFD \) can justify the following theorem:
Responses:
- ASA (Angle-Side-Angle)
- SSA (Side-Side-Angle)
- AAS (Angle-Angle-Side)
- SSS (Side-Side-Side)
- HL (Hypotenuse-Leg for right triangles)
- SAS (Side-Angle-Side)
Correct Response:
For congruence via the transformations mentioned, the SAS (Side-Angle-Side) theorem is typically the one used since once you orient and position the triangles correctly, you can compare corresponding sides and angles.
So, for question 2, the answer is SAS.