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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 which answers are truly correct and why be smart

Dilation
Dilation

Rotation
Rotation

Translation
Translation

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

ASA
ASA

SSA
SSA

AAS
AAS

SSS
SSS

HL
HL

SAS
SAS
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1 answer

To show that triangle \( \triangle ABC \) is congruent to triangle \( \triangle EFD \) by mapping \( ABC \) on top of \( EFD \), we would need to perform transformations that ensure the corresponding sides and angles are congruent.

Transformations

The following transformations are relevant for demonstrating the congruence of triangles:

  1. Translation: This moves the triangle without changing its shape or size.
  2. Rotation: This rotates the triangle around a point, maintaining the size and angle measurements.
  3. Reflection: This flips the triangle over a line, again retaining the size and angle measures.

Dilation is not applicable here, as it would change the size of the triangle, affecting the sides and not preserving congruence.

Correct options for transformations:

  • Translation
  • Rotation
  • Reflection

Question 2: What theorem does this justify?

To determine which theorem justifies the congruence, we consider the transformations mentioned above. Each transformation could help in congruent mapping, but we need to consider what is preserved under them:

  • ASA (Angle-Side-Angle): Two angles and the included side are equal.
  • SSA (Side-Side-Angle): Not a congruence theorem since it does not ensure triangle congruence with certainty.
  • AAS (Angle-Angle-Side): Two angles and the non-included side are equal.
  • SSS (Side-Side-Side): All three sides are equal.
  • HL (Hypotenuse-Leg): Specific to right triangles.
  • SAS (Side-Angle-Side): Two sides and the included angle are equal.

If we can show the corresponding sides are congruent via translation and rotation, and the corresponding angles are congruent via these transformations, we can justify the congruence through either SAS, AAS, or SSS depending on what specific lengths and angles are given.

Based on the transformations mentioned, the best fit for transformations leading to congruence can often be captured by AAS, SAS, or SSS, depending on the information provided regarding sides and angles.

Final Response:

  • Transformations: Translation, Rotation, Reflection (Dilation is incorrect)
  • Justified Theorem: Typically would lean towards SAS or AAS if two angles and a side are known, or SSS if all sides are known. The choice may depend on the exact triangle measurements presented, not provided in this interaction.