Question

which congruence theorem can be used to prove △wxs ≅ △yzs?
sss
asa
sas
hl

Explanation:

Step1: Identify the given information

We have two right - angled triangles \(\triangle WXS\) and \(\triangle YZS\). \(\angle WXS=\angle YZS = 90^{\circ}\), \(XS = ZS\) (marked as equal), and \(\angle WSX=\angle YSZ\) (vertically - opposite angles, so \(\angle WSX=\angle YSZ\)).

Step2: Recall the ASA (Angle - Side - Angle) congruence criterion

The ASA congruence criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent.
In \(\triangle WXS\) and \(\triangle YZS\), \(\angle WXS=\angle YZS\), \(XS = ZS\), and \(\angle WSX=\angle YSZ\).

Answer:

ASA