To determine whether \( \triangle ABC \cong \triangle DEF \) by the AAS (Angle-Angle-Side) Theorem, we need to establish that two angles and the corresponding non-included side of one triangle are congruent to those of the other triangle.
- For AAS to apply:
- We need to establish that two angles from triangle \( ABC \) are congruent to two angles from triangle \( DEF \).
- Additionally, we need to show that one side (not included between the two angles) of triangle \( ABC \) is congruent to the corresponding side from triangle \( DEF \).
From the responses provided:
- "No. The ASA Theorem is used." - This would imply that we can conclude congruence based on two angles and the included side, which might be true but doesn't address AAS specifically.
- "No. DE does not correspond to BC." - This suggests a misunderstanding of congruence, focusing on specific sides not aligning.
- "Yes. The AAS Theorem is used." - This suggests that we have established two angles and a corresponding side.
- "Yes. BC ≅ FE." - This indicates a specific side is corresponding and is congruent.
Based on the earlier points, if indeed we can show two angles and the corresponding side leading to either AAS or ASA, we say "Yes. The AAS Theorem is used."
However, without the specific image you mentioned to confirm the angles and sides, I lean towards picking the last option:
Yes. The AAS Theorem is used.
This response correctly aligns with the principles for congruence with the AAS theorem.
1 answer