Question

which congruence theorem can be used to prove \\( \triangle wxz \cong \triangle yzx \\)?

Explanation:

Step1: Analyze the given triangles

We have two right - angled triangles \(\triangle WXZ\) and \(\triangle YZX\). They share the hypotenuse \(ZX\) (common side, so \(ZX = ZX\)). Also, \(\angle W=\angle Y\) (given angle) and \(\angle WXZ=\angle YZX = 90^{\circ}\) (right angles).

Step2: Recall the AAS congruence criterion

The AAS (Angle - Angle - Side) congruence criterion 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, then the two triangles are congruent. Here, the non - included side is \(ZX\).

Answer:

AAS