Question
\(\angle A\cong\angle B\). Do \(\Delta AGF\) and \(\Delta BDE\) meet the AA Criterion? Why or why not?
Option #1: Yes, two angles are congruent.
Option #2: No, side measures are needed.
Option #3: Yes, if one angle is congruent, then all angles are.
Option #4: No, two pairs of corresponding angles need to be congruent.
(1 point)
The correct response is Option #
.
Option #1: Yes, two angles are congruent.
Option #2: No, side measures are needed.
Option #3: Yes, if one angle is congruent, then all angles are.
Option #4: No, two pairs of corresponding angles need to be congruent.
(1 point)
The correct response is Option #
.
Answers
Answered by
GPT-4o mini
To determine if \(\Delta AGF\) and \(\Delta BDE\) meet the AA (Angle-Angle) Criterion, we should recall that the AA Criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.
Since we only know that \(\angle A \cong \angle B\), we do not have enough information about the second angles of each triangle (i.e., we don't know if \(\angle G\) is congruent to \(\angle D\) or if \(\angle F\) is congruent to \(\angle E\)). Therefore, we cannot conclude that \(\Delta AGF\) and \(\Delta BDE\) are similar based solely on the information given (one pair of angles).
Thus, the correct option regarding whether the triangles meet the AA Criterion is:
**Option #4: No, two pairs of corresponding angles need to be congruent.**
Since we only know that \(\angle A \cong \angle B\), we do not have enough information about the second angles of each triangle (i.e., we don't know if \(\angle G\) is congruent to \(\angle D\) or if \(\angle F\) is congruent to \(\angle E\)). Therefore, we cannot conclude that \(\Delta AGF\) and \(\Delta BDE\) are similar based solely on the information given (one pair of angles).
Thus, the correct option regarding whether the triangles meet the AA Criterion is:
**Option #4: No, two pairs of corresponding angles need to be congruent.**