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Use the image to answer the question.

Two similarly shaped and oriented triangles, upper A upper B upper C and upper D upper E upper F are marked for congruence.

Is △ABC≅△DFE by AAS Theorem?

(1 point)
Responses

No. The ASA Theorem is used.
No. The ASA Theorem is used.

No. DE¯¯¯¯¯¯¯¯ does not correspond to BC¯¯¯¯¯¯¯¯.
No. Modifying above upper D upper E with bar does not correspond to Modifying above upper B upper C with bar .

Yes. BC¯¯¯¯¯¯¯¯≅FE¯¯¯¯¯¯¯¯.
Yes. Modifying above upper B upper C with bar congruent to Modifying above upper F upper E with bar .

Yes. The AAS Theorem is used.
Yes. The AAS Theorem is used.
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1 answer

To determine if \( \triangle ABC \cong \triangle DFE \) by the AAS (Angle-Angle-Side) Theorem, we need to confirm that two angles and the included side are congruent in both triangles.

From your responses, it's indicated that there may be some confusion about the corresponding sides and angles.

  1. The AAS Theorem requires two angles and the side opposite one of those angles to be congruent.
  2. If we found that \( BC \cong FE \), and we also know at least two angles in both triangles are congruent, then we can conclude \( \triangle ABC \cong \triangle DFE \) by AAS.

Based on the provided statements, if:

  • \( BC \cong FE \) is established,
  • and the necessary angles in both triangles are congruent,

Then the statement "Yes. The AAS Theorem is used." would be appropriately applied.

If either of the conditions for AAS (angles and corresponding sides) is not satisfied, then the statement "No. DE does not correspond to BC." could also be an appropriate response.

Without the image to reference, if the angles and sides correspond accurately, you would choose "Yes. The AAS Theorem is used." If not, select the appropriate response indicating the mismatch.