Question

which postulate or theorem proves that these two triangles are congruent? hl congruence theorem aas congruence theorem asa congruence postulate sas congruence postulate

Explanation:

Step1: Recall congruence theorems

• HL (Hypotenuse - Leg): Applies to right - angled triangles. There is no indication that these are right - angled triangles.
• AAS (Angle - Angle - Side): States that if two angles and a non - included side of one triangle are equal to two angles and the corresponding non - included side of another triangle, the triangles are congruent.
• ASA (Angle - Side - Angle): Requires two angles and the included side.
• SAS (Side - Angle - Side): Requires two sides and the included angle.

Step2: Analyze the given triangles

In \(\triangle WXZ\) and \(\triangle WYZ\), we have \(\angle X=\angle Y\), \(\angle WXZ=\angle WYZ\) (the angles at \(W\) and \(Z\) are common in a sense, and we can consider two angles and a non - included side (the side \(WZ\) is common)).

Answer:

B. AAS Congruence Theorem