Question

$\overline{ru}\cong\overline{sv},\angle u\cong\angle v$, and $\overline{ru}\parallel\overline{sv}$. complete the proof that $\triangle rsu\cong\triangle stv$.

Explanation:

Step1: Identify given info

$\overline{RU} \cong \overline{SV}$, $\angle U \cong \angle V$, $\overline{RU} \parallel \overline{SV}$ (Given)

Step2: Find vertical angles

$\angle SRU \cong \angle TSV$ (Vertical angles are congruent)

Step3: Apply ASA congruence

$\triangle RSU \cong \triangle STV$ (ASA: $\angle U \cong \angle V$, $\overline{RU} \cong \overline{SV}$, $\angle SRU \cong \angle TSV$)

Answer:

1. Given
2. Given
3. Given
4. Vertical angles are congruent
5. ASA Congruence Criterion

$\triangle RSU \cong \triangle STV$