Question

cw: triangle congruence theorems
if not congruent, write none in both slots.
these triangles can be proven congruent by □ △rus ≅ △□

Explanation:

Step1: Identify the congruent sides and angles

From the figure, we know that \(SR = ST\) (marked as equal), \(SU = SU\) (common side), and \(\angle RSU=\angle TSU\) (marked as equal).

Step2: Apply the congruence theorem

By the Side - Angle - Side (SAS) congruence theorem, if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.
For \(\triangle RUS\) and \(\triangle TUS\), we have \(SR = ST\), \(\angle RSU=\angle TSU\), and \(SU = SU\). So, \(\triangle RUS\cong\triangle TUS\) by SAS.

Answer:

These triangles can be proven congruent by \(SAS\). \(\triangle RUS\cong\triangle TUS\)