Question

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

Explanation:

Step1: Analyze the given triangles

We have two right - angled triangles \( \triangle WXZ\) and \( \triangle YZX\).
In \( \triangle WXZ\) and \( \triangle YZX\):

• \( \angle WXZ=\angle YZX = 90^{\circ}\) (right angles)
• \( \angle WZX=\angle YXZ\) (given as angles in the figure)
• \( XZ = ZX\) (common side)

Step2: Recall the AAS congruence theorem

The AAS (Angle - Angle - Side) 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