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The AAS Congruence Theorem Quick Check

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Question
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

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

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

To determine whether \( \triangle ABC \cong \triangle DFE \) by the AAS (Angle-Angle-Side) Theorem, we need to first state what AAS means. The AAS Theorem states that if in two triangles, two angles and the non-included side of one triangle are equal to two angles and the corresponding non-included side of the other triangle, then the triangles are congruent.

Given the options and information you've shared, we need to check if two angles and the side opposite one of those angles in \( \triangle ABC \) correspond to the same in \( \triangle DFE \).

The correct responses can be assessed as follows:

  1. Yes. BC ≅ FE. - This suggests the side \( BC \) is congruent to \( FE \), which implies we're using the non-included side correctly.

  2. No. DE does not correspond to BC. - This suggests there's a misunderstanding of which sides correspond between both triangles.

  3. No. The ASA Theorem is used. - This could be misleading as we are specifically evaluating AAS versus ASA.

  4. Yes. The AAS Theorem is used. - If the angles and sides relation holds, this is a valid conclusion.

Given these points, without the visual context confirming angles and sides, the correct match will depend on the relationships in the triangles:

  • If you do have two corresponding angles and a corresponding non-included side that are congruent, then the answer would be: "Yes. The AAS Theorem is used."

If they do not have matching sides and angles corresponding as needed, then you may need to select: "No. DE does not correspond to BC."

Make sure to verify which sides and angles correspond correctly based on the image provided in your question.