Question

19 what else would need to be congruent to show that △ abc ≅ △ xyz by aas? given: ∠a ≅ ∠x, ac ≅ xz a. overline{bc} ≅ overline{xy} b. ∠b ≅ ∠y c. ∠c ≅ ∠z d. overline{ac} ≅ overline{xz}

Explanation:

Step1: Recall AAS Congruence

AAS (Angle - Angle - Side) congruence states that if two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, the triangles are congruent.

Given that $\angle A\cong\angle X$ (right angles) and we know that $AC\cong XZ$ (marked as congruent). We already have one angle and one side. To apply AAS, we need another pair of angles. The angles at $C$ and $Z$ ($\angle C$ and $\angle Z$) are the non - right angles, and if $\angle C\cong\angle Z$, along with $\angle A\cong\angle X$ and $AC\cong XZ$, we can use AAS.

Let's analyze the other options:

• Option A: $\overline{BC}\cong\overline{XY}$ would be more related to HL (Hypotenuse - Leg) or SAS, not AAS.
• Option B: $\angle B\cong\angle Y$: If we use $\angle A\cong\angle X$, $\angle B\cong\angle Y$ and a side, but the side $AC$ and $XZ$ are included between $\angle A$ and $\angle C$ (or $\angle X$ and $\angle Z$), so this would not fit AAS.
• Option D: $AC\cong XZ$ is already given, so it's not what we need to show for AAS.

Answer:

C. $\angle C\cong\angle Z$