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Use the image to answer the question. Is △ABC≅△DFE by AAS Theorem? (1 point) Responses Yes. The AAS Theorem is used. Yes. The AAS Theorem is used. 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 . No. DE¯¯¯¯¯¯¯¯ does not correspond to BC¯¯¯¯¯¯¯¯.

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To determine if △ABC≅△DFE by the AAS (Angle-Angle-Side) Theorem, we first need to confirm if two angles and the non-included side of one triangle are congruent to their counterparts in the other triangle.

  1. AAS Theorem states that if two angles and the non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.
  2. ASA Theorem (Angle-Side-Angle) states that if two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle, then the triangles are congruent.

In your prompt, it seems you are considering the congruence of corresponding angles and sides between the two triangles.

If the correspondence demonstrates that two angles and a non-included side in △ABC are congruent to two angles and the non-included side in △DFE respectively, then the answer would be "Yes. The AAS Theorem is used."

However, if the context suggests that the included sides are being compared instead, or if the setup indicates a violation of the AAS criteria (like two angles with included side being congruent), the correct response would then align with the ASA Theorem instead.

Therefore, based on the typical intention of the question, the responses would be:

  • If it's clear that two angles and a corresponding non-included side are identified as congruent, select: Yes. The AAS Theorem is used.
  • If the configuration indicates the use of included sides, select: No. The ASA Theorem is used.

Without seeing the image or having specifics on the angles and sides, it's difficult to provide a definitive answer between those two.