Question

overleftrightarrow { u w } parallel overleftrightarrow { r t }. complete the proof that angle q s r cong angle w v x.

1 overleftrightarrow { u w } parallel overleftrightarrow { r t } given
2 angle w v x cong angle t s v
3 angle t s v cong angle q s r
4 angle q s r cong angle w v x

Explanation:

Step1: Identify reason for Step 2

Since $\overrightarrow{UW} \parallel \overrightarrow{RT}$ and $\angle WVX$ and $\angle TSV$ are corresponding angles, use Corresponding Angles Theorem.

Step2: Identify reason for Step 3

$\angle TSV$ and $\angle QSR$ are vertical angles, so they are congruent by Vertical Angles Congruence Theorem.

Step3: Conclude final congruence

By Transitive Property of Congruence (if $\angle WVX \cong \angle TSV$ and $\angle TSV \cong \angle QSR$, then $\angle QSR \cong \angle WVX$).

Answer:

• Step 2 reason: Corresponding Angles Theorem
• Step 3 reason: Vertical Angles Congruence Theorem
• Step 4 reason: Transitive Property of Congruence

Final conclusion: $\angle QSR \cong \angle WVX$ is proven.