Question

complete the proof that (overline{tu} cong overline{su}).
image of triangle rst with u on st, angles at s and t marked equal, angles at sru and tru marked equal, and a table with statements and reasons: 1. (angle s cong angle t) (given), 2. (angle sru cong angle tru) (given), 3. (overline{ru} cong overline{ru}), 4. (\triangle rsu cong \triangle rtu), 5. (overline{tu} cong overline{su})

Explanation:

Step1: Identify common side

$\overline{RU} \cong \overline{RU}$ (Reflexive Property of Congruence: a segment is congruent to itself)

Step2: Prove triangle congruence

$\triangle RSU \cong \triangle RTU$ (AAS Congruence: two angles and a non-included side of one triangle are congruent to the corresponding parts of the other triangle; we have $\angle S \cong \angle T$, $\angle SRU \cong \angle TRU$, and $\overline{RU} \cong \overline{RU}$)

Step3: Corresponding parts of congruent triangles

$\overline{TU} \cong \overline{SU}$ (CPCTC: Corresponding Parts of Congruent Triangles are Congruent)

Answer:

Statement	Reason
2. $\angle SRU \cong \angle TRU$	Given
3. $\overline{RU} \cong \overline{RU}$	Reflexive Property of Congruence
4. $\triangle RSU \cong \triangle RTU$	AAS Triangle Congruence Postulate
5. $\overline{TU} \cong \overline{SU}$	CPCTC (Corresponding Parts of Congruent Triangles are Congruent)