Question

as shown in the diagram below, $overline{wy}$ bisects $angle xwz$ and $angle x cong angle z$. based on the information provided, which theorem could be used to prove $\triangle wxy cong \triangle wzy$? options: aas, sss, ...

Explanation:

Step1: Analyze Given Information

We know \( \overline{WY} \) bisects \( \angle XWZ \), so \( \angle XWY=\angle ZWY \). Also, \( \angle X \cong \angle Z \), and \( \overline{WY} \) is common to both \( \triangle WXY \) and \( \triangle WZY \).

Step2: Identify Congruence Criterion

For triangle congruence, AAS (Angle - Angle - Side) 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. Here, we have \( \angle X \cong \angle Z \), \( \angle XWY=\angle ZWY \), and \( \overline{WY} \cong \overline{WY} \) (common side, non - included between the two angles). So the AAS criterion applies.

Answer:

AAS (assuming the option with AAS is the correct one, e.g., if the options are like A. AAS, B. SSS, C. ASA, then the answer is A. AAS)