Question

what additional information could be used to prove that $\triangle xyzcong\triangle feg$ using asa or aas? check all that apply. $angle zcongangle g$ and $overline{xz}congoverline{fg}$ $angle zcongangle g$ and $angle ycongangle e$ $overline{xz}congoverline{fg}$ and $overline{zy}congoverline{ge}$ $overline{xy}congoverline{ef}$ and $overline{zy}congoverline{fg}$ $angle zcongangle g$ and $overline{xy}congoverline{fe}$

Explanation:

Step1: Recall ASA and AAS criteria

ASA (Angle - Side - Angle) requires two pairs of congruent angles and the included side congruent. AAS (Angle - Angle - Side) requires two pairs of congruent angles and a non - included side congruent.

Step2: Analyze each option

• For $\angle Z\cong\angle G$ and $\overline{XZ}\cong\overline{FG}$, with an additional pair of angles, it can be ASA or AAS.
• For $\angle Z\cong\angle G$ and $\angle Y\cong\angle E$, with a side congruence, it can be AAS.
• $\overline{XZ}\cong\overline{FG}$ and $\overline{ZY}\cong\overline{GE}$ is SSS or SAS not ASA or AAS.
• $\overline{XY}\cong\overline{EF}$ and $\overline{ZY}\cong\overline{FG}$ is SSS or SAS not ASA or AAS.
• $\angle Z\cong\angle G$ and $\overline{XY}\cong\overline{FE}$ is not a valid combination for ASA or AAS.

Answer:

$\angle Z\cong\angle G$ and $\overline{XZ}\cong\overline{FG}$, $\angle Z\cong\angle G$ and $\angle Y\cong\angle E$