Question

which congruence theorem can be used to prove $\triangle wxz \cong \triangle yzx$?
options: aas, asa, sas, hl

Explanation:

Step1: Identify the given information

We have two right - angled triangles \(\triangle WXZ\) and \(\triangle YZX\).
We know that \(\angle WXZ=\angle YZX = 90^{\circ}\) (right angles), \(\angle WZX=\angle YXZ\) (given angles), and \(XZ = ZX\) (common side).

Step2: Recall the AAS (Angle - Angle - Side) congruence theorem

The AAS congruence theorem 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.
In \(\triangle WXZ\) and \(\triangle YZX\), we have two angles (\(\angle WXZ=\angle YZX\) and \(\angle WZX=\angle YXZ\)) and a non - included side (\(XZ\)) that are equal.

Answer:

A. AAS