What transformations need to be done in order show that △ABC≅△EFD

To show that triangle ( \triangle ABC ) is congruent to triangle ( \triangle EFD ) by mapping ( ABC ) on top of ( EFD ), you typically need to determine the transformations that achieve this congruence. In general, the possible transformations that could be used are:

1. Reflection: This may be necessary if the triangles are mirrored versions of each other.
2. Rotation: This is used if the triangles need to be rotated to match.
3. Translation: This is typically used to move one triangle to the position of the other.
4. Dilation: This changes the size of a triangle and is not applicable for congruence, as congruent triangles are of the same size.

For your question, the relevant transformations are usually Reflection, Rotation, and Translation (but not Dilation).

For the second part of your question regarding the theorem that justifies the congruence, the most commonly applicable theorems based on transformations are:

• SAS (Side-Angle-Side): If you can show that two sides and the included angle are congruent, the triangles are congruent.
• ASA (Angle-Side-Angle): Two angles and the side between them are congruent.
• SSS (Side-Side-Side): All three sides of one triangle are congruent to all three sides of another triangle.
• AAS (Angle-Angle-Side): Two angles and a non-included side are congruent.
• HL (Hypotenuse-Leg): This is specifically for right triangles.

You will need to determine which congruence theorem can be justified by the specific transformations used while mapping one triangle over the other. If the triangles are being mapped exactly without altering their size, SAS or ASA is likely the justification depending on the specific sides and angles involved.

If you provide more details about the triangles or the information available (such as side lengths or angles), I can give a more definitive answer regarding which theorem applies.