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)ResponsesNo. The ASA Theorem is used.No. The ASA Theorem is used.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 .Yes. BC¯¯¯¯¯¯¯¯≅FE¯¯¯¯¯¯¯¯.

Answer 1

The AAS (Angle-Angle-Side) theorem states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

To determine if triangles \( \triangle ABC \) and \( \triangle DFE \) are congruent by AAS, we need to check:

1. If two angles from \( \triangle ABC \) are congruent to two angles from \( \triangle DFE \).
2. The side that lies between those two angles in one triangle is congruent to the corresponding side in the other triangle.

From the given information, it seems that the responses are assessing various aspects of the congruence arguments.

Without the image, I can't definitively state the congruence based on specific angles and sides. However, based on your question, if it's stated that "Yes. The AAS Theorem is used" in one of the responses, that could imply that there exists enough evidence of angle and side relationships to conclude congruence by AAS.

However, if any response indicates a mismatch in corresponding sides or angles, then the conclusion regarding congruence would not hold.

If you were to choose an option, the most correct response would be:

• Yes. The AAS Theorem is used.

But verify based on the specifics of your triangles \( \triangle ABC \) and \( \triangle DFE \).