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

Answer 1

To determine whether the triangles \( \triangle ABC \) and \( \triangle DFE \) are congruent by the Angle-Angle-Side (AAS) theorem, we need to consider the conditions of AAS. AAS states that if two angles and the side opposite one of those angles in one triangle are congruent to the corresponding angles and the side in another triangle, then the triangles are congruent.

However, since you mentioned two options related to the congruence of sides and the use of the AAS and ASA (Angle-Side-Angle) theorems, let's break it down:

• AAS Theorem: Requires two angles and a non-included side to be congruent.
• ASA Theorem: Requires two angles and the included side to be congruent.

In your statement, if we are comparing the segments \( BC \) and \( FE \) and questioning their congruence with the mention of \( DE \) not corresponding to \( BC \), we should conclude on that basis.

Therefore, the appropriate response is:

No. \( \overline{DE} \) does not correspond to \( \overline{BC} \).