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 .
Yes. The AAS Theorem is used.
Yes. The AAS 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 .
No. The ASA Theorem is used.
No. The ASA Theorem is used.
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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 .
Yes. The AAS Theorem is used.
Yes. The AAS 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 .
No. The ASA Theorem is used.
No. The ASA Theorem is used.
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Answers
GPT-4o mini
To determine if triangles \( \triangle ABC \) and \( \triangle DEF \) are congruent by the AAS (Angle-Angle-Side) theorem, we need to analyze the information provided.
The AAS theorem states that if we know 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 two triangles are congruent.
1. If you are given that two angles of triangle \( ABC \) are congruent to two angles of triangle \( DEF \) and the corresponding sides opposite one of the angles are congruent, then we can conclude \( \triangle ABC \cong \triangle DEF \) by the AAS theorem.
2. However, if the side that corresponds to the two triangles does not match, like \( \overline{DE} \) not corresponding to \( \overline{BC} \), then we cannot use the AAS theorem.
Given the options provided, the correct choice would be:
- **No. \( \overline{DE} \) does not correspond to \( \overline{BC} \).**
This indicates that the sides being compared for congruence do not match in terms of their corresponding triangles, which means the AAS theorem cannot be applied here.
The AAS theorem states that if we know 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 two triangles are congruent.
1. If you are given that two angles of triangle \( ABC \) are congruent to two angles of triangle \( DEF \) and the corresponding sides opposite one of the angles are congruent, then we can conclude \( \triangle ABC \cong \triangle DEF \) by the AAS theorem.
2. However, if the side that corresponds to the two triangles does not match, like \( \overline{DE} \) not corresponding to \( \overline{BC} \), then we cannot use the AAS theorem.
Given the options provided, the correct choice would be:
- **No. \( \overline{DE} \) does not correspond to \( \overline{BC} \).**
This indicates that the sides being compared for congruence do not match in terms of their corresponding triangles, which means the AAS theorem cannot be applied here.