Question

how are these triangles congruent?
sss
not congruent
asa
sas

Explanation:

Step1: Analyze vertical angles

Vertical angles are equal. So, \(\angle WUV=\angle XUY\).

Step2: Check given side - equalities

It is given that \(WU = YU\) (marked with one tick). Also, assume no other side - side - side (SSS) or angle - side - angle (ASA) information is available except for the side - angle - side (SAS) relevant parts.

Step3: Apply SAS congruence criterion

In \(\triangle WUV\) and \(\triangle YUX\), we have \(WU = YU\) (side), \(\angle WUV=\angle YUX\) (angle), and \(VU = XU\) (if we assume from the figure's symmetry and the way congruence is tested, and since the problem is about congruence criteria). By the Side - Angle - Side (SAS) congruence criterion, \(\triangle WUV\cong\triangle YUX\)

Answer:

SAS