Question

proving congruency using asa and aas congruence theorems
what additional information could be used to prove that △xyz≅△feg using asa or aas? choose two correct answers.
∠z≅∠g and xy≅fe
∠z≅∠g and xz≅fg
xz≅fg and zy≅ge
∠z≅∠g and ∠y≅∠e

Explanation:

Step1: Recall ASA and AAS congruence

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

Step2: Analyze each option

• For $\angle Z\cong\angle G$ and $\overline{XY}\cong\overline{FE}$, this is not ASA or AAS as the side is not correctly positioned relative to the angles.
• For $\angle Z\cong\angle G$ and $\overline{XZ}\cong\overline{FG}$, if we assume we have another pair of angles (either $\angle X\cong\angle F$ or $\angle Y\cong\angle E$), it can be AAS.
• For $\overline{XZ}\cong\overline{FG}$ and $\overline{ZY}\cong\overline{GE}$, this is SSS (Side - Side - Side) not ASA or AAS.
• For $\angle Z\cong\angle G$ and $\angle Y\cong\angle E$, if we assume we have a pair of non - included sides congruent, it can be AAS.

Answer:

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