Question

what additional information could be used to prove that δxyz ≅ δfeg using asa or aas? check all that apply. ∠z ≅ ∠g and xz ≅ fg ∠z ≅ ∠g and ∠y ≅ ∠e xz ≅ fg and zy ≅ ge xy ≅ ef and zy ≅ fg ∠z ≅ ∠g and xy ≅ 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 could be AAS. But alone, it's not enough for ASA or AAS.
• For $\angle Z\cong\angle G$ and $\angle Y\cong\angle E$, with two pairs of angles, if we assume some side - angle relationship (non - included side for AAS), this can be used for AAS.
• For $\overline{XZ}\cong\overline{FG}$ and $\overline{ZY}\cong\overline{GE}$, this is SSS (Side - Side - Side) or SAS (Side - Angle - Side) related, not ASA or AAS.
• For $\overline{XY}\cong\overline{EF}$ and $\overline{ZY}\cong\overline{FG}$, this is SSS or SAS related, not ASA or AAS.
• For $\angle Z\cong\angle G$ and $\overline{XY}\cong\overline{FE}$, with an additional pair of angles, it could be AAS.

Answer:

B. $\angle Z\cong\angle G$ and $\angle Y\cong\angle E$
E. $\angle Z\cong\angle G$ and $\overline{XY}\cong\overline{FE}$