Question

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

Explanation:

Step1: Identify the right angles

In \(\triangle WXS\) and \(\triangle YZS\), \(\angle WXS=\angle YZS = 90^{\circ}\) (given as right - angles).

Step2: Analyze the vertical angles

\(\angle WSW=\angle YSZ\) (vertical angles are equal).

Step3: Analyze the equal sides

Since \(XS = ZS\) (marked as equal in the figure).
We have two right - angled triangles (\(\angle WXS=\angle YZS = 90^{\circ}\)), a pair of equal sides (\(XS = ZS\)) and a pair of equal angles (\(\angle WSW=\angle YSZ\)). By the ASA (Angle - Side - Angle) congruence theorem, \(\triangle WXS\cong\triangle YZS\).

Answer:

ASA