Question

$\overline{rv} \cong \overline{sv}$ and $\overline{tv} \cong \overline{uv}$. complete the proof that $\triangle ruv \cong \triangle stv$.

statement
reason
1
$\overline{rv} \cong \overline{sv}$

2
$\overline{tv} \cong \overline{uv}$

3
$\angle rvu \cong \angle svt$

4
$\triangle ruv \cong \triangle stv$

Explanation:

1. The statement $\overline{RV} \cong \overline{SV}$ is provided as a given condition in the problem.
2. The statement $\overline{TV} \cong \overline{UV}$ is also a given condition from the problem.
3. $\angle RVU$ and $\angle SVT$ are vertical angles, and vertical angles are always congruent by the Vertical Angles Congruence Theorem.
4. We have two pairs of congruent sides ($\overline{RV} \cong \overline{SV}$, $\overline{TV} \cong \overline{UV}$) and the included congruent angles ($\angle RVU \cong \angle SVT$), so the Side-Angle-Side (SAS) Congruence Postulate proves $\triangle RUV \cong \triangle STV$.

Answer:

1. Given
2. Given
3. Vertical Angles Congruence Theorem
4. SAS Congruence Postulate