Question

1. $overline{st} cong overline{tu}$; reason: given
2. $angle rts cong angle qtu$; reason: given
3. $overline{st} perp overline{rs}$; reason: given
4. $overline{qu} perp overline{tu}$; reason: given
5. $angle u cong angle s$; reason: all right angles are congruent
6. $\triangle rst cong \triangle qut$; reason: to be filled

Explanation:

Step1: Identify Congruent Parts

We have $\overline{ST} \cong \overline{TU}$ (Step 1), $\angle RTS \cong \angle QTU$ (Step 2), and $\angle U \cong \angle S$ (Step 5, right angles congruent).

Step2: Determine Congruence Criterion

This matches the Angle - Side - Angle (ASA) congruence criterion, where two angles and the included side of one triangle are congruent to two angles and the included side of another triangle. For $\triangle RST$ and $\triangle QUT$: $\angle S \cong \angle U$ (right angles), $\overline{ST} \cong \overline{TU}$ (given), and $\angle RTS \cong \angle QTU$ (given). So the reason is ASA (Angle - Side - Angle) Congruence Postulate.

Answer:

Angle - Side - Angle (ASA) Congruence Postulate