Question$R$ is the midpoint of $\overline{Q S}, \overline{Q T} \cong \overline{R U}$, and $\overline{S U} \cong \overline{R T}$. Complete the proof that $\triangle Q R T \cong \triangle R S U$. \begin{tabular}{|l|l|l|l|} \hline & Statement & Reason \\ \hline 1 & $R$ is the midpoint of $\overline{Q S}$ & \\ 2 & $\overline{Q T} \cong \overline{R U}$ & & $=$ \\ 3 & $\overline{S U} \cong \overline{R T}$ & & $=$ \\ 4 & $\overline{Q R} \cong \overline{R S}$ & & $=$ \\ 5 & $\triangle Q R T \cong \triangle R S U$ & & $=$ \\ \hline \end{tabular}

Studdy Solution
Use the given congruences and the congruence from the midpoint to apply a triangle congruence theorem:
We have the following congruences:
1. $\overline{Q R} \cong \overline{R S}$ (from Step 1)
2. $\overline{Q T} \cong \overline{R U}$ (given)
3. $\overline{S U} \cong \overline{R T}$ (given)
Using the Side-Side-Side (SSS) Congruence Theorem, which states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent, we can conclude:
$$\triangle Q R T \cong \triangle R S U$$
The proof is complete with the statement:
$$\boxed{\triangle Q R T \cong \triangle R S U}$$