Question

What transformations need to be done in order show that △ABC≅△EFD
by mapping ABC on top of EFD? Check all that apply



(4 points)
Responses

Translation
Translation

Reflection
Reflection

Dilation
Dilation

Rotation
Rotation
Question 2
What theorem does this justify?(1 point)
Responses

ASA
ASA

SSA
SSA

AAS
AAS

SAS
SAS

SSS
SSS

HL
HL
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Answers

GPT-4o mini
To show that triangle \( \triangle ABC \) is congruent to triangle \( \triangle EFD \) by mapping \( ABC \) on top of \( EFD \), the transformations that could be used typically include:

1. **Translation** - This is often necessary if the triangles are in different locations.
2. **Reflection** - This may be needed if the triangles are mirrored.
3. **Rotation** - This can help align the triangles properly without altering their shape or size.

Each transformation can help align two triangles in space, establishing their congruence after potentially applying one, two, or a combination of these transformations.

Based on the options, **Dilation** would **not** be appropriate since dilation changes the size of the figure, and congruence requires the figures to be the same size.

### Answer for Transformations:

- **Translation**: Check
- **Reflection**: Check
- **Dilation**: Uncheck
- **Rotation**: Check

### Answer for the Theorem:

The congruence can typically be justified by one of several triangle congruence theorems depending on the context and information given about the triangles (like side lengths and angles). Without specific details about the triangles' measures, the most relevant options that involve transformations would be:

The most general congruence theorems applicable here would be:
- **SAS (Side-Angle-Side)**: If the triangles can be shown to have two pairs of sides and the included angle congruent through transformations.
- **ASA (Angle-Side-Angle)**: If the triangles show two pairs of angles and the included side congruent through transformations.

Assuming that the transitions apply correctly and with sufficient checks on sides and angles, the justification could relate to **SAS** or **ASA** based on how the triangles line up after transformations.

Since no specific numbers or angles are provided, it would depend on the given details.

### Finalized Responses:
1. Transformations: Translation, Reflection, Rotation
2. Theorem Justified: ASA (if two angles and the included side are used) or SAS (if two sides and the included angle).

If a single response is needed, then **SAS** or **ASA** would suffice based on context!

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