Question

u is the midpoint of \\( \overline{qs} \\) and \\( \overline{rt} \\). complete the proof that \\( \triangle qtu \cong \triangle sru \\).

Explanation:

Step1: Recall the SSS (Side - Side - Side) Congruence Theorem

The SSS congruence theorem states that if three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.

Step2: Identify the congruent sides

We are given that \(\overline{QT}\cong\overline{RS}\) (Statement 3). From the definition of mid - point (\(U\) is the mid - point of \(\overline{QS}\)), we have \(\overline{QU}\cong\overline{SU}\) (Statement 4). Also, since \(U\) is the mid - point of \(\overline{RT}\), we have \(\overline{RU}\cong\overline{TU}\) (Statement 5).

Answer:

By the SSS (Side - Side - Side) congruence theorem.