Question

Is △ABC≅△DFE by AAS Theorem? (1 point) Responses 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 . No. The ASA Theorem is used. No. The ASA Theorem is used. 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.

Answer 1

To determine if triangles △ABC and △DFE are congruent by the AAS (Angle-Angle-Side) theorem, we need to establish if the two triangles have at least two angles and the included side congruent.

1. **Identify Angles and Sides**: Check if:
- Two angles of △ABC are congruent to two angles of △DFE.
- The side between those two angles in one triangle is equal to the corresponding side in the other triangle.

2. **Examining the Responses**:
- The responses allude to checking correspondences of sides and angles.
- References to the ASA theorem indicate that the congruence conditions selected are based on angles and a side but not necessarily in the way AAS would require.

3. **Conclusion**: Without knowing the specific measurements or congruencies given in your problem, you cannot definitively conclude the congruence of these two triangles using just AAS or ASA. But the correct approach for confirming congruence is:
- Proving two angles and the included side of one triangle are congruent to the corresponding parts of another triangle for ASA.
- Proving two angles and a non-included side for AAS.

If you have the angles and sides specified explicitly in a "Yes" or "No" format, please provide that data to analyze the congruence correctly. Based on your initial responses, if angles and corresponding sides are congruent as stated, then **Yes** could be a valid conclusion by the appropriate theorem depending on which angles and side are considered.