Question

7
given: $overline{su}$ and $rt$ bisect each other; $overline{st} cong overline{ur}$
prove: $angle stv cong angle urv$

statements	reasons
2. $overline{sv} = overline{uv}$; $overline{rv} cong overline{tv}$	2.
3.	3. given
4.	4. side - side - side (sss)
5. $angle stv cong angle urv$	5.

Explanation:

Step1: State given reason

Reason for Statement 1: Given

Step2: Define bisector segment congruence

Reason for Statement 2: Definition of segment bisector (bisectors split segments into two congruent parts)

Step3: Insert given congruent sides

Statement 3: $\overline{ST} \cong \overline{UR}$

Step4: List all congruent triangle sides

Statement 4: $\triangle STV \cong \triangle URV$

Step5: CPCTC for congruent angles

Reason for Statement 5: Corresponding Parts of Congruent Triangles are Congruent (CPCTC)

Answer:

Statements	Reasons
2. $\overline{SV} \cong \overline{UV}; \overline{RV} \cong \overline{TV}$	2. Definition of segment bisector
3. $\overline{ST} \cong \overline{UR}$	3. Given
4. $\triangle STV \cong \triangle URV$	4. Side-Side-Side (SSS)
5. $\angle STV = \angle URV$	5. Corresponding Parts of Congruent Triangles are Congruent (CPCTC)