Question

Is \(\triangle ABC\cong\triangle DFE\) by AAS Theorem?
(1 point)
Yes. The AAS Theorem is used.
No. \(\overline{DE}\) does not correspond to \(\overline{BC}\).
Yes. \(\overline{BC}\cong\overline{FE}\).
No. The ASA Theorem is used.

Answer 1

To determine whether \(\triangle ABC \cong \triangle DFE\) by the AAS (Angle-Angle-Side) theorem, we first need to understand what the theorem states: two triangles are congruent if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

In the options you've provided:

1. **Yes. The AAS Theorem is used.** - This may be true if we have the correct angles and the corresponding side.
2. **No. \(\overline{DE}\) does not correspond to \(\overline{BC}\).** - This suggests a misalignment in corresponding sides, which would invalidate congruence.
3. **Yes. \(\overline{BC}\cong\overline{FE}\).** - This is also true if \(\overline{BC}\) and \(\overline{FE}\) are corresponding sides.
4. **No. The ASA Theorem is used.** - If two angles and the included side are given, this would be the appropriate theorem.

To apply the AAS theorem correctly, angles and their corresponding sides should be accurately determined. However, without a diagram or specific angle/side relationships, we can't definitively conclude.

Based on the provided options:
- If AAS holds true, select **"Yes. The AAS Theorem is used."**
- If there is confusion about corresponding sides, possibly select **"No. \(\overline{DE}\) does not correspond to \(\overline{BC}\)."**
- Verify if you have the corresponding sides and angles correct.

Thus, the answer most commonly used when assessing this without further details would be: **Yes. The AAS Theorem is used.** if angles and a non-included side align properly, otherwise choose the option about corresponding sides or the right theorem as applicable.