Question

s is the midpoint of \\(\overline{rt}\\), \\(\overline{ru} \cong \overline{sv}\\), and \\(\overline{tv} \cong \overline{su}\\). complete the proof that \\(\triangle rsu \cong \triangle stv\\).

statement	reason
2. \\(\overline{ru} \cong \overline{sv}\\)	given
3. \\(\overline{tv} \cong \overline{su}\\)	given
4. \\(\overline{rs} \cong \overline{st}\\)	definition of midpoint
5

Explanation:

Step1: List given side congruences

1. $\overline{RU} \cong \overline{SV}$ (Given)
2. $\overline{TV} \cong \overline{SU}$ (Given)
3. $\overline{RS} \cong \overline{ST}$ (Definition of midpoint)

Step2: Apply SSS congruence rule

If all three pairs of corresponding sides of two triangles are congruent, the triangles are congruent by the Side-Side-Side (SSS) Congruence Postulate.
So, $\triangle RSU \cong \triangle STV$ by SSS.

Answer:

$\triangle RSU \cong \triangle STV$