Question

state what additional information is required to prove δstu ≅ δums by sss.

Explanation:

Step1: Recall SSS congruence condition

SSS (Side - Side - Side) congruence states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

Step2: Analyze the given sides

From the figure, we know that \(TS = US\) (marked with one tick) and \(MS=US\) (marked with one tick). The common side for \(\triangle STU\) and \(\triangle UMS\) is \(SU\). But for SSS, we need \(TU = UM\) as the third pair of equal sides.

Answer:

The additional information required is \(TU = UM\)