Question

u is the midpoint of \\(\overline{st}\\). complete the proof that \\(\triangle rtu \cong \triangle rsu\\).

statement	reason
2 \\(\overline{st} \perp \overline{ru}\\)	given
3 \\(\angle rus \cong \angle rut\\)	all right angles are congruent
4 \\(\overline{su} \cong \overline{tu}\\)	definition of midpoint
5

Explanation:

Step1: Identify shared side

$\overline{RU} \cong \overline{RU}$

Step2: Apply SAS congruence

$\Delta RTU \cong \Delta RSU$

Step3: State reasons

Reason for $\overline{RU} \cong \overline{RU}$: Reflexive Property of Congruence; Reason for $\Delta RTU \cong \Delta RSU$: Side-Angle-Side (SAS) Congruence Postulate

Answer:

$\overline{RU} \cong \overline{RU}$; $\Delta RTU \cong \Delta RSU$